Applying biclustering algorithms for specifying partial rankings based on RUR data

Workflow

1. Loading Libraries and Data

• Loading Necessary Libraries
• Normalize
• Loading Necessary Data

2. Estimation of the Number of Biclusters

• Seriation of Data
• Seriation of Normalized Data
• Estimating the Number of Biclusters

3. Applying iBBiG on Normalized Data

• Calculating Top League A Bicluster
• Calculating F-tests of the Top League A Bicluster
• Heat Maps of the Top League A
• Checking the Stability of the Top League A Bicluster
• The Impact of Changing the Threshold
• Calculating Partial Rankings
• Comparing Partial Rankings to the Adequate Part of the Original Ranking
• Summary of Findings about League A

4. Applying iBBiG on reversed normalized data

• Calculating Lower League C Bicluster
• Calculating F-tests of the Lower League C Bicluster
• Heat Maps of the Lower League C
• Checking the Stability of the Lower League C Bicluster
• The Impact of Changing the Threshold
• Calculating Partial Rankings
• Comparing Partial Rankings to the Adequate Part of the Original Ranking
• Summary of Findings about League C

5. Applying BicARE

• Calculating Middle League B Bicluster
• Calculating F-tests of the Middle League B Bicluster
• Heat Maps of the Middle League B
• Checking the Stability of the Middle League B Bicluster
• Calculating Partial Rankings
• Comparing Partial Rankings to the Adequate Part of the Original Ranking
• Summary of Findings about League B

6. Specifying Overlaps

• Venn Diagram of Indicators
• Venn Diagram of HEIs

7. Summing up the Conclusions

Loading Libraries and Data

Loading Necessary Libraries

#Seriation and biclustering
library(seriation) #For seriate a matrix
library(biclust) #General biclustering functions
library(iBBiG) #iBBiG biclustering
library(BicARE) #BicARE biclustering
library(BcDiag) #Diagnostics of biclusters

#Additional statistic packages
library(factoextra) #Additional distance functions
library(corrgram) #Correlation diagram
library(VennDiagram) #VennDiagram
library(venneuler) #VennDiagram

#For formatted and interactive tables and figures
library(knitr) #Formatted tables, figures

#Read Excel file
library(readxl) #Read Excel file

Citations

#Seriation and biclustering
print(citation("seriation"),style="text") #For seriate a matrix

## Hahsler M, Buchta C, Hornik K (2019). _seriation: Infrastructure for
## Ordering Objects Using Seriation_. R package version 1.2-8, <URL:
## https://CRAN.R-project.org/package=seriation>.
## 
## Hahsler M, Hornik K, Buchta C (2008). "Getting things in order: An
## introduction to the R package seriation." _Journal of Statistical
## Software_, *25*(3), 1-34. ISSN 1548-7660, <URL:
## http://www.jstatsoft.org/v25/i03/>.

print(citation("biclust"),style="text") #General biclustering functions

## Kaiser S, Santamaria R, Khamiakova T, Sill M, Theron R, Quintales L,
## Leisch F, De Troyer. E (2020). _biclust: BiCluster Algorithms_. R
## package version 2.0.2, <URL:
## https://CRAN.R-project.org/package=biclust>.

print(citation("iBBiG"),style="text") #iBBiG biclustering

## Gusenleitner D, Culhane A (2020). _iBBiG: Iterative Binary Biclustering
## of Genesets_. R package version 1.32.0, <URL:
## http://bcb.dfci.harvard.edu/~aedin/publications/>.

print(citation("BicARE"),style="text") #BicARE biclustering

## Gestraud P (2020). _BicARE: Biclustering Analysis and Results
## Exploration_. R package version 1.46.0, <URL: http://bioinfo.curie.fr>.

print(citation("BcDiag"),style="text") #Diagnostics of biclusters

## Mengsteab A, Otava M, Khamiakova T, De Troyer E (2015). _BcDiag:
## Diagnostics Plots for Bicluster Data_. R package version 1.0.10, <URL:
## https://CRAN.R-project.org/package=BcDiag>.

#Additional statistic packages
print(citation("factoextra"),style="text") #Additional distance functions

## Kassambara A, Mundt F (2020). _factoextra: Extract and Visualize the
## Results of Multivariate Data Analyses_. R package version 1.0.7, <URL:
## https://CRAN.R-project.org/package=factoextra>.

print(citation("VennDiagram"),style="text") #VennDiagram

## Chen H (2018). _VennDiagram: Generate High-Resolution Venn and Euler
## Plots_. R package version 1.6.20, <URL:
## https://CRAN.R-project.org/package=VennDiagram>.

print(citation("venneuler"),style="text") #VennDiagram

## Wilkinson L (2011). _venneuler: Venn and Euler Diagrams_. R package
## version 1.1-0, <URL: https://CRAN.R-project.org/package=venneuler>.

#For formatted and interactive tables and figures
print(citation("knitr"),style="text") #Formatted tables, figures

## Xie Y (2020). _knitr: A General-Purpose Package for Dynamic Report
## Generation in R_. R package version 1.29, <URL:
## https://yihui.org/knitr/>.
## 
## Xie Y (2015). _Dynamic Documents with R and knitr_, 2nd edition.
## Chapman and Hall/CRC, Boca Raton, Florida. ISBN 978-1498716963, <URL:
## https://yihui.org/knitr/>.
## 
## Xie Y (2014). "knitr: A Comprehensive Tool for Reproducible Research in
## R." In Stodden V, Leisch F, Peng RD (eds.), _Implementing Reproducible
## Computational Research_. Chapman and Hall/CRC. ISBN 978-1466561595,
## <URL: http://www.crcpress.com/product/isbn/9781466561595>.

#Read Excel file
print(citation("readxl"),style="text") #Read Excel file

## Wickham H, Bryan J (2019). _readxl: Read Excel Files_. R package
## version 1.3.1, <URL: https://CRAN.R-project.org/package=readxl>.

Normalize

normalize <- function(x) {
return ((x - min(x)) / (max(x) - min(x)))
}

Loading Necessary Data

data<-read_excel("RUR2020.xlsx")
RUR<-data[,2:21]
rownames(RUR)<-as.matrix(data[,1])
weights=c(0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02)
rownames(RUR)<-as.matrix(data[,1])
orig_mtx<-as.matrix(RUR)

for (i in 1:ncol(RUR)){ #Normalize (min-max)
  RUR[,i]<-normalize(RUR[,i])
}
rownames(RUR)<-as.matrix(data[,1])
mtx<-as.matrix(RUR)

weights<-matrix(weights,1,20)
colnames(weights)<-colnames(RUR)

BR<-rowSums(RUR*weights)/max(rowSums(RUR*weights))

RANK_RUR<-as.matrix(rank(-BR))
rownames(RANK_RUR)<-rownames(RUR)

Estimation of the Number of Biclusters

Seriation of Data

Firstly, to obtain a preliminary picture of the possible biclusters, the seriation of the original data is done.

ORIG_SER <- c(seriate(get_dist(orig_mtx,"euclidean"),method="HC_COMPLETE"),seriate(get_dist(t(orig_mtx),"spearman"),method="HC_COMPLETE"))
ORIG_ORDERED<-orig_mtx[get_order(ORIG_SER,dim=1),get_order(ORIG_SER,dim=2)]
rownames(ORIG_ORDERED) <- rownames(mtx[get_order(ORIG_SER,dim=1),get_order(ORIG_SER,dim=2)])

After seriation, plotting the heat map of the original data (see Fig. 1) can help to detect the possible biclusters. On Fig. 1 blue cells indicate a lower value of the indicators, and red cells mean a higher value of the indicators.

hmap(as.matrix(ORIG_ORDERED),col=bluered(100),showdist="both")

Fig. 1 Heat map of the original matrix after seriation

Seriation of Normalized Data

After the normalization of the original data, seriation is done on the normalized data.

ALL_SER <- c(seriate(get_dist(mtx,"euclidean"),method="HC_COMPLETE"),seriate(get_dist(t(mtx),"spearman"),method="HC_COMPLETE"))
ALL_ORDERED<-mtx[get_order(ALL_SER,dim=1),get_order(ALL_SER,dim=2)]
rownames(ALL_ORDERED) <- rownames(mtx[get_order(ALL_SER,dim=1),get_order(ALL_SER,dim=2)])

Estimating the Number of Biclusters

After seriation, plotting the heat map of the normalized original data (see Fig. 2) can help to detect the possible biclusters.

hmap(as.matrix(ALL_ORDERED),col=bluered(100),showdist="both")

Fig. 2 Heat map of the normalized and seriated matrix

After seriation, two bigger homogeneous blocks can be identified based on Fig. 2. The block of the red cells on the top left corner on Fig. 2 indicates the top league, while the bigger blue block, which indicates the remaining (lower) league, can be discovered in the bottom of the figure. The dendrogram of two-way clustering also shows that regarding rows and columns two main blocks can be specified.

Applying iBBiG on Normalized Data

Applying the iBBiG method on the original normalized data can specify the top league biclusters. First of all, the number of biclusters needed to be determined. Since Fig. 2 indicates that there are two biclusters, the algorithm is set to search for two biclusters.

Results should satisfy three criteria.

1. A bicluster (i.e. the result) should be significant both for rows and for columns. (The linearity is not required (see Tukey tests).)
2. A bicluster should be stable both for columns and for rows.
3. The bicluster should store the essence of the information of the database.

res <- iBBiG(binaryMatrix=binarize(mtx,threshold = 0.50),nModules = 2,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done
## Module:  2 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## Number of Clusters found:  2 
## 
## First  2  Cluster scores and sizes:
##                         M 1 M 2
## Cluster Score      3800.414 682
## Number of Rows:     398.000 341
## Number of Columns:   17.000   2

The results above show that the iBBiG algorithm found 2 biclusters. In the first bicluster there are 398 rows (HEIs) and 17 columns (indicators), in the second bicluster there are 341 rows (HEIs) and only 2 columns (indicators). The next step is to calculate F-tests to determine which bicluster is significant.

Obs.FStat <- NULL
for (i in c(1:res@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=res,number=i)
}
kable(Obs.FStat,caption = "**Table 1** The results of row and column effects for two biclusters")

Table 1 The results of row and column effects for two biclusters

Fstat PValue Row Effect 5.493095 0 Column Effect 15.719947 0 Tukey test 65.132550 0

Fstat PValue Row Effect 3.6722027 0.0000000 Column Effect 0.5767775 0.4481045 Tukey test 0.1148022 0.7349516

In Table 1 the results of the F-tests can be seen. In the case of the first bicluster, both the row and column effect are significant. On the other hand, in the case of the second bicluster the column effect is not significant; thus the second bicluster is not significant. Only the first one which is the top league (League A).

Calculating Top League A Bicluster

The next step is to identify the top league bicluster.

res <- iBBiG(binaryMatrix=binarize(mtx,threshold = 0.50),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 3800.414 and 
##   398 Rows and  17 columns

The results of the iBBiG algorithm can be seen above. The algorithm found one bicluster in which there are 398 rows (HEIs) and 17 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant or not.

Calculating F-tests of the Top League A Bicluster

Table 2 contains the results of the row and column effects (F-tests). Both the row and column effects are significant, so the top league bicluster is significant.

Obs.FStat <- NULL
for (i in c(1:res@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=res,number=i)
}
kable(Obs.FStat,caption = "**Table 2** The results of row and column effects for the top league")

Table 2 The results of row and column effects for the top league

Fstat PValue Row Effect 5.493095 0 Column Effect 15.719947 0 Tukey test 65.132550 0

To see the differences between those HEIs that are included in the top league and those that are not, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 3). (The horizontal axis of Fig. 3 shows the HEIs, the vertical axis shows the mentioned parameters on normalized (0-1) data of indicators.) On Fig. 3 the red line indicates those HEIs that are included in the top league, while the black line shows the remaining ones. The HEIs in the top league have higher means and medians, and have lower variances.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 3 Mean, median, variance and MAD for the top league HEIs

One can do the same for the columns (indicators). Fig. 4 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. (The horizontal axis of Fig. 4 shows the indicators, the vertical axis shows the mentioned parameters on normalized (0-1) data of HEIs.) The red line indicates those indicators that are in the top league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 4 Mean, median, variance and MAD for the top league indicators

Heat Maps of the Top League A

Fig. 5 depicts the heat map of the top league. The top league contains 398 HEIs and 17 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=res,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 5 Heat map of the top league

Fig. 6 shows the heat map of the results of iBBiG on normalized data. The top league can be seen in the upper left corner of Fig. 6 which is enlarged on Fig.5.

drawHeatmap(x=mtx,bicResult=res,local=FALSE,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 6 Heat map of the output after applying iBBiG on normalized data

Checking the Stability of the Top League A Bicluster

The next step is to check the stability of the top league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=res,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 0.8567413 0.8015801
##   [2,] 1.0333993 1.2065612
##   [3,] 1.0907091 0.8251378
##   [4,] 0.9378042 0.6282656
##   [5,] 0.9344028 0.6168177
##   [6,] 1.0198377 1.1099949
##   [7,] 1.0282310 1.8912026
##   [8,] 0.9020868 0.9650731
##   [9,] 1.0132411 0.6927305
##  [10,] 0.9836213 0.9833376
##  [11,] 1.0978562 0.8378473
##  [12,] 1.0018528 0.7637394
##  [13,] 0.9950505 0.6851625
##  [14,] 0.8586476 1.2698852
##  [15,] 0.9609317 0.7814653
##  [16,] 1.0836800 0.7644586
##  [17,] 0.9941068 0.8720624
##  [18,] 1.0796817 1.4934862
##  [19,] 0.9948879 0.6400309
##  [20,] 1.0366808 1.0271849
##  [21,] 0.9271867 0.9490565
##  [22,] 0.9388592 0.6554214
##  [23,] 1.0152078 1.0001148
##  [24,] 1.0574091 0.8191604
##  [25,] 0.9831607 1.3971517
##  [26,] 1.0828712 0.8493565
##  [27,] 0.9380831 1.0670718
##  [28,] 0.9553970 1.3550519
##  [29,] 1.0316912 0.7158740
##  [30,] 1.0847669 1.5648162
##  [31,] 0.9849539 1.5584701
##  [32,] 1.0002999 2.0038843
##  [33,] 0.8291127 0.7544299
##  [34,] 1.1450477 1.8417058
##  [35,] 0.8874329 0.8062261
##  [36,] 1.0018814 0.9754306
##  [37,] 1.1115475 0.6963376
##  [38,] 0.9355497 1.0569967
##  [39,] 1.0733362 1.1146352
##  [40,] 0.9083783 0.9766254
##  [41,] 1.1139115 0.8288935
##  [42,] 0.8567582 1.1877672
##  [43,] 0.9775843 0.5807187
##  [44,] 0.9713328 0.7248465
##  [45,] 0.8640019 0.6159062
##  [46,] 0.9379093 0.6037256
##  [47,] 1.0096264 0.4730906
##  [48,] 0.8894358 1.1204576
##  [49,] 0.9805928 0.6420976
##  [50,] 0.8901526 0.7287168
##  [51,] 0.9648614 1.8428160
##  [52,] 1.0300576 1.4538765
##  [53,] 0.9653455 1.2440006
##  [54,] 0.9330579 1.3233216
##  [55,] 1.1252599 0.4540160
##  [56,] 1.0453811 0.9526425
##  [57,] 1.0763233 0.6689776
##  [58,] 1.1016849 1.4417445
##  [59,] 0.9326832 1.0044247
##  [60,] 0.9221618 1.0682969
##  [61,] 1.0466892 0.9960076
##  [62,] 0.9883497 1.2025508
##  [63,] 0.9900812 1.3639671
##  [64,] 0.9749196 1.0057894
##  [65,] 0.9693387 1.6802966
##  [66,] 0.9013353 1.3743798
##  [67,] 1.1228828 1.2314506
##  [68,] 1.0346074 0.4918790
##  [69,] 1.0029188 1.0236935
##  [70,] 0.9574911 0.6966757
##  [71,] 0.9402446 0.4837700
##  [72,] 1.1377979 0.6474217
##  [73,] 0.7898119 0.8105623
##  [74,] 0.9660480 0.6597814
##  [75,] 0.8417114 1.0426298
##  [76,] 0.9554751 1.0696729
##  [77,] 0.9157553 1.0535780
##  [78,] 0.9894749 1.0985186
##  [79,] 0.9692788 0.4885682
##  [80,] 1.0439931 0.8754855
##  [81,] 0.9701386 0.9120197
##  [82,] 0.9471128 0.8625284
##  [83,] 1.0588824 0.9388912
##  [84,] 0.9423393 0.9241453
##  [85,] 0.9369801 1.0101233
##  [86,] 0.9833776 0.7317260
##  [87,] 1.1215319 0.4254307
##  [88,] 0.9267913 1.3222263
##  [89,] 0.9527213 0.6281157
##  [90,] 0.9886211 1.0076872
##  [91,] 1.0048222 0.9494206
##  [92,] 1.1724809 0.6675181
##  [93,] 1.0520626 1.2219618
##  [94,] 0.9020677 1.3082034
##  [95,] 1.0067603 0.2901890
##  [96,] 0.9008385 1.1338204
##  [97,] 1.1917828 0.4811526
##  [98,] 1.0578120 1.4622498
##  [99,] 1.0668260 0.4029044
## [100,] 0.8915667 1.3723343
## 
## $observedFstatRow
## [1] 5.493095
## 
## $observedFstatCol
## [1] 15.71995
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

Since the bootstrapPvalueCol and the bootstrapPvalueRow are lower than 0.01, the bicluster is stable both for rows and columns.

The Impact of Changing the Threshold

The change of the threshold shows its impacts on leagues. The thresholds are in 0.75 (specifies Q1 leagues) 0.9 (specifies D1 leagues).

The Q1 League A

Calculating the Top Q1 League A Bicluster

The next step is to identify the top Q1 league bicluster.

res <- iBBiG(binaryMatrix=binarize(mtx,threshold = 0.75),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 931.9664 and 
##   174 Rows and  11 columns

The results of the iBBiG algorithm can be seen above. The algorithm found one bicluster in which there are 174 rows (HEIs) and 11 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant or not.

Calculating F-tests of the Top Q1 League A Bicluster

In Table 3 the results of the row and column effects (F-tests) can be read. Both the row and column effects are significant, so the top league bicluster is significant.

Obs.FStat <- NULL
for (i in c(1:res@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=res,number=i)
}
kable(Obs.FStat,caption = "**Table 3** The results of row and column effects for the top (Q1) league")

Table 3 The results of row and column effects for the top (Q1) league

Fstat PValue Row Effect 2.7503411 0.0000000 Column Effect 7.5663208 0.0000000 Tukey test 0.9457689 0.3309347

To see the differences between the HEIs included in the top league and those that are not, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 7). (The horizontal axis of Fig. 7 shows the HEIs, the vertical axis shows the mentioned parameters on normalized (0-1) data of indicators.) On Fig. 7 the red line indicates the HEIs that are included in the top Q1 league, while the black line shows the remaining ones. The HEIs in the top league have higher means and medians, and have lower variances.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 7 Mean, median, variance and MAD for the top Q1 league HEIs

One can do the same for the indicators (columns). Fig. 8 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. (The horizontal axis of Fig. 8 shows the indicators, the vertical axis shows the mentioned parameters on normalized (0-1) data of HEIs.) The red line indicates those indicators that are in the top Q1 league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 8 Mean, median, variance and MAD for the top Q1 league indicators

Heat Maps of the Top Q1 League A Bicluster

Fig. 9 depicts the heat map of the Q1 league. The top league contains 174 HEIs and 11 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=res,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 9 Heat map of the top Q1 league

Fig. 10 shows the heat map of the results of iBBiG on normalized data. The Q1 league can be seen in the upper left corner of Fig. 10 which is enlarged on Fig. 9.

drawHeatmap(x=mtx,bicResult=res,local=FALSE,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 10 Heat map of the output after applying iBBiG on normalized data

Checking the Stability of the Top Q1 League A Bicluster

The next step is to check the stability of the top league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=res,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 1.1579947 1.3456193
##   [2,] 1.0839181 0.7184744
##   [3,] 1.2381227 0.6086841
##   [4,] 0.9803542 1.3071414
##   [5,] 0.9389292 1.2572703
##   [6,] 1.1821951 0.9892932
##   [7,] 1.0248464 2.3819726
##   [8,] 0.9160080 0.6281436
##   [9,] 0.9681516 0.7046989
##  [10,] 1.1007210 0.4976811
##  [11,] 1.1544031 1.1759539
##  [12,] 0.9805132 1.3800485
##  [13,] 0.9574123 2.3888927
##  [14,] 1.1374882 0.6689617
##  [15,] 1.0054892 1.2632241
##  [16,] 0.8912969 0.8807569
##  [17,] 0.9635593 0.2203682
##  [18,] 0.8280377 0.6253376
##  [19,] 0.9787934 0.3759661
##  [20,] 0.9372352 2.2521315
##  [21,] 0.9530510 1.9238823
##  [22,] 1.1018099 2.1402004
##  [23,] 1.1172453 0.6416205
##  [24,] 0.9597821 1.4179111
##  [25,] 1.1323246 0.1836555
##  [26,] 0.9036496 1.7713816
##  [27,] 1.0220095 0.6650437
##  [28,] 1.0713469 1.2831315
##  [29,] 0.8741905 0.4651470
##  [30,] 0.9542494 1.1773603
##  [31,] 1.0167619 1.1664800
##  [32,] 0.9526437 0.6461009
##  [33,] 0.9835952 0.5292828
##  [34,] 0.9803033 0.3683470
##  [35,] 0.8941417 0.8333491
##  [36,] 1.1433197 1.2337024
##  [37,] 0.8711999 1.7343882
##  [38,] 1.0125789 0.8048978
##  [39,] 0.8900679 0.9444113
##  [40,] 0.9531680 2.3702862
##  [41,] 0.8655910 0.7605027
##  [42,] 0.9642718 2.2690002
##  [43,] 1.0152435 1.1450417
##  [44,] 0.8293105 0.4900405
##  [45,] 0.8567544 0.9336362
##  [46,] 1.1018618 1.6042595
##  [47,] 1.0092460 1.7636379
##  [48,] 1.1722939 1.2542923
##  [49,] 0.8571061 0.8870300
##  [50,] 0.7965205 0.7330724
##  [51,] 1.0614184 0.4606481
##  [52,] 1.0224335 1.0919767
##  [53,] 0.8834527 0.6829612
##  [54,] 1.1359707 0.7608206
##  [55,] 1.2760031 1.1154140
##  [56,] 1.1653939 1.8986412
##  [57,] 1.2100121 1.6820794
##  [58,] 0.9659323 0.5683547
##  [59,] 1.1498814 0.6947413
##  [60,] 1.1792068 0.7025637
##  [61,] 1.0194932 1.2549059
##  [62,] 0.7152743 0.7150892
##  [63,] 1.1037417 0.8639237
##  [64,] 1.0023851 0.9148449
##  [65,] 1.0904031 0.6999390
##  [66,] 0.9930231 0.7376333
##  [67,] 1.0031208 1.7302302
##  [68,] 0.9181981 0.4511811
##  [69,] 0.9440708 0.5869553
##  [70,] 1.0339000 1.1539890
##  [71,] 1.0176838 1.8374468
##  [72,] 0.8465794 0.9524592
##  [73,] 1.0301757 1.2233020
##  [74,] 1.0915721 0.9752492
##  [75,] 0.8575810 0.6671803
##  [76,] 0.9869160 2.3745661
##  [77,] 0.8897452 0.4004813
##  [78,] 1.0738642 1.1019694
##  [79,] 0.9002620 1.8977953
##  [80,] 1.0316231 0.8592926
##  [81,] 1.0474879 1.1780757
##  [82,] 1.0135009 0.8896523
##  [83,] 0.8705818 1.1855950
##  [84,] 0.8345104 0.8232391
##  [85,] 0.9859138 0.5287192
##  [86,] 1.0144643 1.6693757
##  [87,] 0.9198969 0.8329045
##  [88,] 0.9499256 1.4476715
##  [89,] 0.9356167 0.6588382
##  [90,] 0.8552329 0.7454264
##  [91,] 1.0462457 0.8481503
##  [92,] 1.0182781 0.4262309
##  [93,] 1.0545027 1.1877264
##  [94,] 1.2465668 1.2988764
##  [95,] 1.0165341 1.0002438
##  [96,] 0.9478269 0.8556397
##  [97,] 0.9773944 1.2298550
##  [98,] 1.0194300 0.3485497
##  [99,] 0.9982812 0.7350042
## [100,] 0.8901907 1.5827742
## 
## $observedFstatRow
## [1] 2.750341
## 
## $observedFstatCol
## [1] 7.566321
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

Since the bootstrapPvalueCol and the bootstrapPvalueRow are lower than 0.01, the bicluster is stable.

Calculating Partial Rankings for Top Q1 league A

The next step is to calculate partial rankings based on the indicators and HEIs in the top league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 4 shows the result of partial ranking in the case of the top league.

C<-biclust::bicluster(mtx,res,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 4** League A by iBBiG",digits = 2)

Table 4 League A by iBBiG

	T3	T4	T5	R1	R3	R4	R5	I4	F1	F2	F4	Overall_Score	Rank
USA_Rockefeller University	0.52	0.00	0.75	0.96	1.00	0.68	0.80	0.83	0.99	1.00	0.98	0.86	74
USA_Vanderbilt University	0.46	0.94	0.89	0.77	0.93	0.62	0.88	0.83	0.56	0.95	0.80	0.80	128
USA_Emory University	0.61	0.95	0.90	0.80	0.92	0.66	0.89	0.87	0.95	0.98	0.80	0.86	75
Israel_Weizmann Institute of Science	0.88	0.00	0.64	0.92	0.98	0.76	0.81	0.83	0.95	0.99	0.65	0.74	159
USA_Johns Hopkins University	0.49	0.96	0.98	0.92	0.95	0.85	0.98	0.98	0.96	0.98	0.99	0.92	27
Switzerland_University of Zurich	0.46	0.93	0.87	0.75	0.92	0.62	0.89	0.88	0.27	0.77	0.48	0.72	162
USA_University of Rochester	0.48	0.82	0.76	0.79	0.89	0.66	0.79	0.82	0.97	0.98	0.82	0.80	126
USA_Yale University	0.71	0.97	0.99	0.95	0.96	0.90	0.99	0.99	0.98	0.99	0.87	0.99	4
Japan_Tohoku University	0.48	0.87	0.91	0.63	0.37	0.72	0.91	0.85	0.50	0.88	0.78	0.73	160
USA_University of Pittsburgh	0.58	0.88	0.93	0.80	0.91	0.66	0.92	0.93	0.55	0.89	0.77	0.84	95
USA_Columbia University	0.68	0.99	0.99	0.84	0.97	0.68	0.98	0.98	0.89	0.96	0.83	0.91	38
USA_University of Chicago	0.71	0.96	0.98	0.99	0.99	0.93	0.99	0.99	0.96	0.98	0.83	0.95	15
USA_California Institute of Technology (Caltech)	0.91	0.98	0.99	1.00	0.99	0.99	0.99	0.99	0.99	0.99	0.94	1.00	1
USA_University of Pennsylvania	0.83	0.95	0.98	0.93	0.95	0.87	0.98	0.97	0.99	0.99	0.86	0.95	14
Denmark_Technical University of Denmark	0.61	0.88	0.79	0.82	0.80	0.76	0.82	0.84	0.56	0.87	0.91	0.82	114
Italy_Scuola Normale Superiore di Pisa	0.97	0.99	0.73	1.00	0.98	0.99	0.67	0.72	0.76	0.93	0.31	0.81	123
Russia_Lomonosov Moscow State University	0.79	0.88	0.95	0.52	0.31	0.61	0.94	0.90	0.69	0.89	0.94	0.82	108
USA_Stanford University	0.88	0.98	1.00	0.97	0.99	0.87	1.00	1.00	0.99	0.99	0.85	0.99	3
USA_University of California, San Diego	0.42	0.60	0.96	0.79	0.96	0.60	0.96	0.96	0.87	0.94	0.81	0.87	63
Japan_Osaka University	0.57	0.83	0.91	0.68	0.33	0.75	0.92	0.84	0.59	0.86	0.82	0.74	158
USA_Washington University in St. Louis	0.86	0.96	0.93	0.94	0.97	0.85	0.93	0.91	0.96	0.97	0.85	0.95	12
USA_Dartmouth College	0.50	0.74	0.84	0.92	0.88	0.93	0.69	0.75	0.88	0.95	0.87	0.89	48
China_University of Science and Technology of China	0.88	0.97	0.66	0.91	0.81	0.90	0.66	0.62	0.79	0.92	0.97	0.89	50
Japan_Tokyo Institute of Technology	0.62	0.92	0.93	0.76	0.35	0.85	0.92	0.91	0.43	0.78	0.86	0.76	151
USA_University of California, Los Angeles	0.64	0.75	0.99	0.86	0.93	0.76	0.99	0.99	0.92	0.96	0.80	0.87	65
Japan_Hokkaido University	0.59	0.84	0.82	0.62	0.29	0.76	0.82	0.69	0.52	0.81	0.78	0.70	167
USA_Princeton University	0.78	0.91	0.99	0.96	0.99	0.88	0.99	0.99	0.97	0.97	0.85	0.94	16
USA_University of Michigan	0.69	0.85	0.99	0.85	0.89	0.78	0.99	0.98	0.83	0.92	0.82	0.89	46
USA_Georgetown University	0.91	0.96	0.84	0.53	0.79	0.44	0.82	0.87	0.78	0.90	0.67	0.82	110
USA_Massachusetts Institute of Technology (MIT)	0.89	0.97	1.00	0.90	1.00	0.62	1.00	1.00	0.99	0.99	0.93	0.99	5
USA_Case Western Reserve University	0.92	0.97	0.79	0.90	0.89	0.87	0.79	0.81	0.84	0.92	0.91	0.90	44
USA_New York University	0.70	0.89	0.96	0.67	0.94	0.57	0.97	0.97	0.92	0.95	0.69	0.88	54
USA_Rice University	0.68	0.84	0.85	0.90	0.98	0.79	0.84	0.86	0.88	0.93	0.75	0.88	52
Japan_Kyoto University	0.70	0.89	0.97	0.78	0.43	0.83	0.97	0.94	0.74	0.89	0.81	0.79	140
Sweden_Karolinska Institute	0.80	0.92	0.92	0.99	0.91	0.98	0.93	0.95	0.84	0.91	0.97	0.95	13
Japan_Nagoya University	0.69	0.85	0.86	0.69	0.40	0.76	0.86	0.75	0.72	0.87	0.87	0.78	143
USA_Harvard University	0.96	0.99	1.00	1.00	0.98	1.00	1.00	1.00	0.97	0.97	0.87	1.00	2
USA_Tufts University	0.93	0.97	0.74	0.84	0.93	0.75	0.72	0.78	0.85	0.91	0.72	0.83	97
Switzerland_University of Lausanne	0.54	0.80	0.64	0.90	0.83	0.88	0.60	0.60	0.51	0.75	0.86	0.69	169
India_Indian Institute of Science	0.97	1.00	0.84	0.94	0.28	0.99	0.85	0.80	0.91	0.93	0.97	0.91	36
USA_University of North Carolina	0.74	0.91	0.95	0.77	0.90	0.65	0.95	0.95	0.82	0.90	0.83	0.90	42
USA_Cornell University	0.76	0.86	0.97	0.96	0.94	0.93	0.97	0.98	0.83	0.90	0.80	0.94	17
USA_University of Wisconsin - Madison	0.80	0.85	0.97	0.73	0.87	0.64	0.97	0.97	0.74	0.87	0.81	0.87	68
Republic of Korea_Korea Advanced Institute of Science and Technology (KAIST)	0.96	0.98	0.93	0.88	0.54	0.93	0.95	0.90	0.93	0.95	0.99	0.91	34
Republic of Korea_Pohang University of Science and Technology	0.98	0.98	0.83	0.97	0.57	0.99	0.87	0.78	0.93	0.95	0.98	0.93	24
UK_University College London	0.80	0.90	0.97	0.90	0.94	0.84	0.97	0.98	0.66	0.82	0.69	0.88	60
Japan_University of Tokyo	0.90	0.94	0.98	0.82	0.52	0.83	0.98	0.97	0.88	0.92	0.82	0.88	58
UK_University of Oxford	0.93	0.94	0.99	0.91	0.98	0.81	0.99	0.99	0.87	0.91	0.73	0.94	20
USA_Brown University	0.80	0.84	0.90	0.97	0.92	0.96	0.91	0.91	0.93	0.94	0.75	0.90	43
China_Zhejiang University	0.90	0.92	0.80	0.92	0.55	0.95	0.78	0.70	0.98	0.98	0.99	0.88	51
USA_University of Minnesota	0.83	0.85	0.94	0.72	0.79	0.66	0.95	0.94	0.79	0.87	0.79	0.87	62
Hong Kong_City University of Hong Kong	0.74	0.51	0.78	0.87	0.86	0.92	0.82	0.76	1.00	0.99	0.82	0.84	87
UK_University of Cambridge	0.96	0.94	1.00	0.92	0.96	0.82	1.00	0.99	0.94	0.94	0.73	0.97	7
China_Shanghai Jiao Tong University	0.83	0.94	0.80	0.82	0.49	0.92	0.82	0.82	0.87	0.91	0.96	0.84	86
USA_University of Washington	0.73	0.80	0.97	0.89	0.97	0.78	0.97	0.96	0.94	0.94	0.89	0.93	21
Taiwan_National Taiwan University	0.55	0.78	0.91	0.77	0.44	0.84	0.91	0.85	0.55	0.72	0.88	0.72	163
USA_University of Illinois at Chicago	0.88	0.91	0.84	0.75	0.74	0.69	0.85	0.87	0.84	0.89	0.63	0.81	124
China_Fudan University	0.85	0.95	0.83	0.87	0.61	0.91	0.83	0.77	0.85	0.89	0.97	0.88	57
USA_Rutgers the State University of New Jersey	0.74	0.77	0.89	0.64	0.72	0.59	0.89	0.90	0.81	0.88	0.73	0.79	135
Switzerland_Ecole Polytechnique Federale de Lausanne	0.88	0.95	0.94	0.90	0.97	0.73	0.95	0.95	0.79	0.86	0.87	0.92	30
UK_Imperial College London	0.94	0.93	0.98	0.96	0.95	0.92	0.98	0.98	0.86	0.89	0.76	0.96	10
China_Peking University	0.94	0.98	0.95	0.83	0.71	0.84	0.95	0.93	0.98	0.98	0.97	0.95	11
USA_Boston University	0.89	0.89	0.91	0.87	0.94	0.77	0.90	0.93	0.82	0.87	0.77	0.90	41
USA_University of Iowa	0.78	0.79	0.86	0.62	0.77	0.55	0.85	0.84	0.92	0.93	0.73	0.83	101
USA_University of Southern California	0.55	0.71	0.93	0.83	0.87	0.74	0.93	0.93	0.93	0.93	0.78	0.89	49
China_Tsinghua University	0.87	0.95	0.96	0.83	0.75	0.84	0.96	0.95	0.96	0.96	0.99	0.93	25
USA_University of California, Davis	0.67	0.63	0.94	0.78	0.82	0.71	0.95	0.95	0.93	0.93	0.83	0.84	92
Republic of Korea_Gwangju Institute of Science and Technology	0.94	0.99	0.19	0.93	0.41	0.98	0.40	0.08	0.95	0.94	0.99	0.79	134
Sweden_Lund University	0.53	0.80	0.88	0.85	0.81	0.82	0.88	0.87	0.48	0.63	0.90	0.79	136
Republic of Korea_Yonsei University	0.81	0.68	0.89	0.88	0.45	0.93	0.88	0.77	0.98	0.97	0.92	0.82	117
USA_North Carolina State University	0.65	0.65	0.86	0.65	0.65	0.67	0.85	0.88	0.81	0.85	0.76	0.78	141
Sweden_Chalmers University of Technology	0.78	0.87	0.75	0.73	0.54	0.78	0.76	0.73	0.63	0.75	0.92	0.78	144
USA_Ohio State University	0.78	0.73	0.94	0.71	0.84	0.63	0.94	0.94	0.94	0.94	0.75	0.87	67
UK_King`s College London	0.73	0.76	0.94	0.86	0.96	0.78	0.94	0.95	0.61	0.72	0.59	0.84	90
Spain_Autonomous University of Barcelona	0.81	0.83	0.81	0.74	0.67	0.75	0.81	0.76	0.26	0.38	0.38	0.66	172
UK_University of Edinburgh	0.75	0.78	0.95	0.84	0.97	0.69	0.94	0.95	0.64	0.75	0.66	0.84	89
USA_Northwestern University	0.96	0.96	0.96	0.97	0.97	0.94	0.96	0.96	0.97	0.96	0.93	0.98	6
Canada_McGill University	0.80	0.77	0.95	0.91	0.80	0.89	0.94	0.96	0.60	0.69	0.78	0.82	115
USA_George Washington University	0.95	0.96	0.79	0.60	0.79	0.56	0.78	0.83	0.80	0.83	0.64	0.77	147
Switzerland_ETH Zurich (Swiss Federal Institute of Technology)	0.94	0.97	0.98	0.96	0.93	0.94	0.98	0.98	0.84	0.85	0.96	0.96	9
France_Sorbonne University	0.87	0.92	0.91	0.91	0.80	0.88	0.90	0.91	0.27	0.35	0.24	0.79	137
UK_University of Southampton	0.74	0.70	0.80	0.91	0.95	0.81	0.83	0.87	0.52	0.62	0.52	0.77	145
Japan_University of Tsukuba	0.83	0.86	0.71	0.72	0.40	0.83	0.72	0.69	0.81	0.83	0.76	0.79	139
USA_Carnegie Mellon University	0.69	0.82	0.96	0.88	0.91	0.82	0.96	0.97	0.92	0.91	0.95	0.91	37
USA_University of Notre Dame	0.90	0.83	0.81	0.81	0.79	0.79	0.82	0.83	0.87	0.88	0.72	0.85	78
Netherlands_University of Twente	0.77	0.81	0.74	0.84	0.58	0.90	0.79	0.82	0.74	0.79	0.94	0.79	132
UK_University of Bristol	0.75	0.66	0.86	0.92	0.96	0.81	0.86	0.89	0.63	0.69	0.62	0.81	119
Netherlands_Utrecht University	0.61	0.67	0.89	0.96	0.88	0.94	0.89	0.90	0.53	0.61	0.88	0.83	102
USA_University of Utah	0.77	0.76	0.79	0.77	0.77	0.70	0.81	0.81	0.96	0.94	0.74	0.83	104
USA_University of California, Berkeley	0.84	0.73	0.99	0.94	0.98	0.82	0.99	0.99	0.89	0.88	0.83	0.92	26
Denmark_Aarhus University	0.59	0.61	0.78	0.90	0.76	0.91	0.80	0.81	0.54	0.61	0.89	0.76	152
Brazil_State University of Campinas (Unicamp)	0.91	0.95	0.85	0.64	0.35	0.82	0.84	0.79	0.80	0.80	0.86	0.81	125
USA_Pennsylvania State University	0.65	0.49	0.95	0.82	0.73	0.82	0.95	0.96	0.97	0.94	0.85	0.84	91
Spain_University of Barcelona	0.81	0.77	0.84	0.88	0.75	0.86	0.83	0.82	0.20	0.20	0.40	0.73	161
China_Nanjing University	0.84	0.92	0.72	0.85	0.65	0.87	0.71	0.69	0.80	0.80	0.90	0.81	120
India_Indian Institute of Technology, Madras	0.88	0.93	0.82	0.40	0.29	0.48	0.80	0.75	0.87	0.84	0.71	0.77	146
Switzerland_University of Geneva	0.73	0.84	0.78	0.95	0.92	0.91	0.77	0.79	0.62	0.65	0.68	0.81	121
Sweden_Royal Institute of Technology (KTH)	0.89	0.90	0.88	0.83	0.62	0.87	0.88	0.91	0.69	0.70	0.90	0.82	111
USA_Syracuse University	0.65	0.60	0.80	0.54	0.93	0.41	0.76	0.80	0.82	0.81	0.50	0.71	166
Republic of Korea_Hanyang University	0.91	0.79	0.69	0.81	0.41	0.93	0.68	0.32	0.92	0.90	0.98	0.83	100
Singapore_Nanyang Technological University	0.83	0.61	0.94	0.93	0.96	0.89	0.94	0.92	0.93	0.91	0.92	0.93	23
Brazil_University of Sao Paulo	0.93	0.94	0.92	0.70	0.34	0.88	0.89	0.89	0.62	0.64	0.94	0.82	116
Germany_Ruprecht Karl University of Heidelberg	0.98	0.93	0.90	0.86	0.94	0.75	0.88	0.89	0.76	0.76	0.64	0.87	61
Canada_University of Calgary	0.77	0.70	0.75	0.83	0.72	0.83	0.75	0.83	0.68	0.68	0.77	0.79	138
USA_University of Colorado	0.68	0.59	0.89	0.71	0.96	0.53	0.90	0.90	0.78	0.76	0.72	0.78	142
Switzerland_University of Bern	0.98	0.94	0.70	0.98	0.90	0.98	0.73	0.67	0.88	0.85	0.78	0.87	69
USA_University of California, Irvine	0.70	0.51	0.82	0.82	0.92	0.70	0.86	0.86	0.94	0.90	0.76	0.83	99
Finland_University of Helsinki	0.79	0.81	0.83	0.95	0.92	0.89	0.85	0.86	0.62	0.61	0.87	0.83	105
USA_Colorado School of Mines	0.68	0.59	0.80	0.82	0.85	0.77	0.77	0.86	0.75	0.74	0.69	0.80	129
USA_University of Florida	0.96	0.86	0.92	0.84	0.65	0.88	0.91	0.92	0.90	0.86	0.97	0.89	47
India_Indian Institute of Technology, Delhi	0.91	0.93	0.84	0.57	0.30	0.77	0.81	0.73	0.90	0.86	0.76	0.76	154
USA_Michigan State University	0.86	0.70	0.93	0.72	0.79	0.72	0.92	0.94	0.88	0.84	0.81	0.84	93
USA_Purdue University	0.72	0.62	0.95	0.86	0.68	0.83	0.95	0.96	0.83	0.79	0.90	0.82	113
Netherlands_Radboud University Nijmegen	0.80	0.78	0.64	0.97	0.88	0.95	0.72	0.74	0.67	0.64	0.85	0.83	103
Australia_Australian National University	0.86	0.77	0.91	0.94	0.89	0.95	0.93	0.94	0.82	0.77	0.93	0.92	31
Singapore_National University of Singapore	0.85	0.65	0.98	0.89	0.82	0.87	0.98	0.96	0.97	0.93	0.92	0.92	32
USA_University of Illinois at Urbana - Champaign	0.70	0.57	0.97	0.91	0.87	0.86	0.97	0.97	0.89	0.83	0.84	0.88	56
Hong Kong_University of Hong Kong	0.93	0.78	0.94	0.95	0.77	0.97	0.93	0.92	0.95	0.90	0.97	0.94	18
USA_Virginia Polytechnic Institute and State University	0.76	0.63	0.87	0.60	0.55	0.66	0.87	0.88	0.79	0.73	0.89	0.75	156
USA_University of Arizona	0.86	0.72	0.88	0.82	0.80	0.77	0.90	0.89	0.86	0.80	0.72	0.85	82
Canada_University of British Columbia	0.77	0.64	0.96	0.92	0.86	0.90	0.96	0.97	0.78	0.71	0.77	0.86	72
Finland_Aalto University	0.81	0.86	0.77	0.86	0.73	0.85	0.79	0.80	0.64	0.58	0.63	0.76	153
Hong Kong_Chinese University Hong Kong	0.87	0.67	0.89	0.95	0.82	0.97	0.89	0.82	0.95	0.90	0.95	0.92	28
Republic of Korea_Sungkyunkwan University	0.86	0.72	0.96	0.93	0.57	0.96	0.96	0.92	0.91	0.84	0.95	0.87	64
Canada_University of Toronto	0.89	0.75	0.97	0.94	0.87	0.92	0.97	0.98	0.82	0.73	0.84	0.91	35
Canada_Universite de Montreal	0.95	0.81	0.80	0.89	0.69	0.91	0.81	0.86	0.79	0.69	0.84	0.87	70
Netherlands_Erasmus University Rotterdam	0.70	0.59	0.85	0.99	0.92	0.97	0.87	0.88	0.72	0.62	0.94	0.83	106
Australia_University of Sydney	0.75	0.66	0.93	0.93	0.85	0.94	0.93	0.95	0.74	0.65	0.74	0.86	76
Netherlands_Wageningen University and Research Center	0.87	0.90	0.90	0.90	0.94	0.84	0.91	0.93	0.91	0.81	0.95	0.92	29
Israel_Technion Israel Institute of Technology	0.77	0.69	0.82	0.76	0.58	0.80	0.87	0.90	0.81	0.68	0.51	0.77	149
Ireland_Trinity College Dublin	0.85	0.65	0.78	0.85	0.81	0.80	0.77	0.81	0.67	0.54	0.73	0.76	150
Israel_Tel Aviv University	0.92	0.76	0.78	0.95	0.57	0.98	0.82	0.87	0.69	0.55	0.83	0.79	130
Turkey_Istanbul Technical University	0.33	0.40	0.81	0.37	0.51	0.30	0.76	0.78	0.99	0.97	1.00	0.66	171
Canada_Western University	0.94	0.74	0.67	0.86	0.64	0.92	0.66	0.76	0.79	0.64	0.76	0.79	133
USA_University of California, Santa Cruz	0.52	0.31	0.76	0.93	1.00	0.71	0.77	0.79	0.87	0.74	0.70	0.72	164
Republic of Korea_Konkuk University	0.89	0.49	0.29	0.82	0.30	0.96	0.25	0.24	0.91	0.79	0.90	0.61	174
Australia_University of Western Australia	0.79	0.50	0.77	0.98	0.83	0.99	0.77	0.83	0.80	0.66	0.88	0.82	118
Netherlands_University of Groningen	0.85	0.67	0.81	0.98	0.86	0.98	0.83	0.83	0.80	0.65	0.96	0.85	80
Canada_University of Ottawa	0.97	0.83	0.75	0.87	0.77	0.90	0.68	0.82	0.75	0.57	0.78	0.82	109
USA_Texas A&M University	0.93	0.69	0.92	0.70	0.59	0.75	0.92	0.94	0.87	0.70	0.84	0.84	96
Canada_Queens University	0.93	0.71	0.65	0.78	0.57	0.86	0.64	0.77	0.86	0.68	0.80	0.75	157
Germany_Karlsruhe Institute of Technology	0.92	0.83	0.86	0.84	0.76	0.83	0.88	0.90	0.89	0.73	0.91	0.87	71
USA_Georgia Institute of Technology	0.90	0.73	0.96	0.74	0.90	0.63	0.96	0.97	0.93	0.81	0.92	0.87	66
USA_University of California, Santa Barbara	0.78	0.40	0.92	0.97	0.97	0.89	0.93	0.94	0.94	0.80	0.90	0.90	40
Germany_University of Ulm	0.99	0.94	0.40	0.98	0.78	0.97	0.35	0.53	0.90	0.71	0.83	0.81	122
Canada_McMaster University	0.92	0.62	0.83	0.99	0.85	0.99	0.83	0.89	0.91	0.75	0.96	0.88	59
Belgium_Vrije Universiteit Brussels (VUB)	0.94	0.84	0.64	0.94	0.68	0.96	0.71	0.73	0.86	0.64	0.93	0.84	85
Germany_University of Gottingen	0.97	0.91	0.86	0.92	0.85	0.91	0.83	0.86	0.86	0.62	0.90	0.91	39
Belgium_University of Antwerp	0.92	0.75	0.53	0.96	0.78	0.96	0.64	0.62	0.76	0.50	0.89	0.77	148
Australia_University of Adelaide	0.91	0.53	0.73	0.97	0.95	0.96	0.76	0.83	0.84	0.58	0.84	0.82	112
Australia_University of Wollongong	0.82	0.44	0.55	0.87	0.79	0.93	0.68	0.75	0.85	0.54	0.65	0.70	168
Australia_Monash University	0.87	0.49	0.91	0.94	0.82	0.95	0.91	0.94	0.88	0.59	0.76	0.82	107
Germany_Ludwig Maximilian University of Munich	0.99	0.95	0.93	0.99	0.89	1.00	0.93	0.93	0.98	0.87	1.00	0.97	8
Germany_Technische Universitat Dresden (TU Dresden)	0.98	0.97	0.73	0.93	0.68	0.94	0.74	0.64	0.87	0.57	0.96	0.84	94
Australia_University of Queensland Australia	0.94	0.55	0.90	0.97	0.82	0.97	0.90	0.92	0.89	0.59	0.83	0.88	55
Australia_University of New South Wales	0.93	0.64	0.88	0.93	0.77	0.96	0.90	0.92	0.90	0.61	0.81	0.86	73
Belgium_Katholieke Universiteit Leuven (KU Leuven)	0.95	0.74	0.92	0.95	0.77	0.95	0.92	0.92	0.87	0.53	0.89	0.86	77
Germany_University of Wurzburg	0.97	0.89	0.49	0.99	0.84	0.98	0.51	0.62	0.84	0.49	0.99	0.83	98
Belgium_Ghent University	0.96	0.75	0.86	0.95	0.77	0.97	0.86	0.87	0.77	0.41	0.88	0.88	53
Belgium_University Catholique de Louvain	0.85	0.69	0.80	0.96	0.89	0.95	0.78	0.80	0.85	0.46	0.96	0.84	88
Germany_University of Munster	0.96	0.90	0.67	0.91	0.74	0.90	0.67	0.68	0.77	0.38	0.76	0.80	127
Germany_Darmstadt University of Technology	0.98	0.85	0.64	0.81	0.43	0.91	0.57	0.66	0.92	0.60	0.96	0.75	155
Australia_Queensland University of Technology	0.81	0.36	0.74	0.79	0.69	0.86	0.69	0.79	0.81	0.41	0.79	0.69	170
Germany_University of Freiburg	1.00	0.89	0.79	0.98	0.74	0.98	0.74	0.79	0.91	0.57	0.98	0.85	79
Germany_Technical University of Munich	0.99	0.91	0.93	0.99	0.74	0.99	0.93	0.94	0.97	0.76	0.98	0.94	19
Germany_Humboldt University of Berlin	0.98	0.88	0.90	0.99	0.82	1.00	0.90	0.90	0.85	0.33	0.71	0.84	83
Germany_University of Konstanz	0.98	0.79	0.58	0.88	0.60	0.94	0.63	0.60	0.91	0.45	0.98	0.79	131
Germany_University of Erlangen Nuremberg	0.99	0.90	0.51	0.98	0.74	0.99	0.60	0.48	0.98	0.74	0.92	0.85	81
Germany_Free University of Berlin	0.99	0.91	0.87	1.00	0.72	1.00	0.88	0.88	0.89	0.37	0.82	0.89	45
Germany_University of Hamburg	1.00	0.85	0.72	0.91	0.82	0.91	0.73	0.75	0.96	0.60	0.80	0.84	84
Germany_Technical University of Berlin	0.99	0.87	0.88	0.88	0.58	0.95	0.87	0.88	0.96	0.58	0.94	0.92	33
Germany_RWTH Aachen University	0.99	0.93	0.86	0.98	0.79	0.98	0.86	0.86	0.95	0.53	0.98	0.93	22
Germany_Bielefeld University	0.92	0.66	0.51	0.89	0.78	0.88	0.51	0.38	0.84	0.25	0.79	0.63	173
Germany_University of Hannover	0.98	0.76	0.58	0.82	0.52	0.92	0.61	0.67	0.94	0.43	0.89	0.71	165

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a weak positive relationship between the two rankings.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.3402887

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 579210, p-value = 4.973e-06
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.3402887

The Top D1 League A

Calculating the Top D1 League A Bicluster

The next step is to identify the D1 top league bicluster.

res <- iBBiG(binaryMatrix=binarize(mtx,threshold = 0.9),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 221.6605 and 
##   78 Rows and  3 columns

The results of the iBBiG algorithm can be seen above. The algorithm found one bicluster in which there are 78 rows (HEIs) and 3 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant or not.

Calculating F-tests of the Top D1 League A Bicluster

In Table 5 the results of the row and column effects (F-tests) can be read. The row effect is significant, however the column effect is insignificant, so the top D1 league bicluster is insignificant.

Obs.FStat <- NULL
for (i in c(1:res@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=res,number=i)
}
kable(Obs.FStat,caption = "**Table 5** The results of row and column effects for the top D1 league")

Table 5 The results of row and column effects for the top D1 league

Fstat PValue Row Effect 20.493072 0.0000000 Column Effect 0.092263 0.9119157 Tukey test 2.168571 0.1429112

To see the differences between those HEIs that are included in the top D1 league and those that are not in the top league, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 11). (The horizontal axis of Fig. 11 shows the HEIs, the vertical axis shows the mentioned parameters on normalized (0-1) data of indicators.) On Fig. 11 the red line indicates those HEIs that are included in the top league, while the black line shows the remaining HEIs. The HEIs in the top league have higher means and medians, and have lower variances.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 11 Mean, median, variance and MAD for the top D1 league HEIs

One can do the same for the columns (indicators). Fig. 12 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. (The horizontal axis of Fig. 12 shows the indicators, the vertical axis shows the mentioned parameters on normalized (0-1) data of HEIs.) The red line indicates those indicators that are in the top league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 12 Mean, median, variance and MAD for the top D1 league indicators

Heat Maps of the Top D1 League A

Fig. 13 depicts the heat map of the top D1 league. The top league contains 78 HEIs and 3 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=res,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 13 Heat map of the top D1 league

Fig. 14 shows the heat map of the results of iBBiG on normalized data. The top league can be seen in the upper left corner of Fig. 14 which is enlarged on Fig. 13.

drawHeatmap(x=mtx,bicResult=res,local=FALSE,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 14 Heat map of the output after applying iBBiG on normalized data

Checking the Stability of the Top D1 League A Bicluster

The next step is to check the stability of the top D1 league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=res,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row    fval.col
##   [1,] 1.2748601 1.299290363
##   [2,] 1.2481137 0.619799638
##   [3,] 1.3401948 0.375051179
##   [4,] 1.0464914 0.121934594
##   [5,] 0.8794696 2.110284853
##   [6,] 1.1396444 0.181662094
##   [7,] 0.9815618 1.810506050
##   [8,] 0.9568158 0.895438880
##   [9,] 0.9644521 4.315125617
##  [10,] 0.8117289 0.229893352
##  [11,] 0.7214852 0.502606759
##  [12,] 1.1449448 0.895557846
##  [13,] 0.8530014 0.003580539
##  [14,] 1.4159630 2.265104945
##  [15,] 1.0360586 2.175279827
##  [16,] 1.1449103 2.163641916
##  [17,] 0.7250780 0.179391495
##  [18,] 1.1043941 0.241580192
##  [19,] 1.0077479 0.457420236
##  [20,] 0.9634349 1.740376898
##  [21,] 0.9024495 0.951915485
##  [22,] 1.2163412 0.448617227
##  [23,] 0.7299669 1.471978574
##  [24,] 0.9716211 0.097952064
##  [25,] 0.7467186 4.189626798
##  [26,] 0.8276446 0.372444515
##  [27,] 0.7457651 0.554695294
##  [28,] 1.2727225 0.782496258
##  [29,] 0.8205354 1.244082247
##  [30,] 0.9380150 0.117319197
##  [31,] 0.8133517 1.675887005
##  [32,] 1.2546210 0.687949071
##  [33,] 0.7353105 0.181414658
##  [34,] 0.8174068 0.056024774
##  [35,] 0.9077768 2.302363571
##  [36,] 0.9334724 0.694454432
##  [37,] 0.9131864 0.460063335
##  [38,] 0.8825889 1.108405733
##  [39,] 0.8298315 0.883122476
##  [40,] 1.2013449 1.364725366
##  [41,] 0.9367246 0.273008129
##  [42,] 1.6231244 0.775581892
##  [43,] 1.1137397 1.779818572
##  [44,] 1.0942777 1.360343562
##  [45,] 0.8438911 0.934737348
##  [46,] 1.0949785 0.016108848
##  [47,] 1.1077686 0.380633108
##  [48,] 1.2349859 0.584191623
##  [49,] 1.0263210 0.034506518
##  [50,] 1.2134804 0.324487207
##  [51,] 1.2312034 4.145796943
##  [52,] 1.4130115 2.124211323
##  [53,] 1.1859677 1.259683830
##  [54,] 0.9634904 0.009343491
##  [55,] 0.7988711 1.985814101
##  [56,] 1.2260282 0.687301488
##  [57,] 0.8256986 0.020982332
##  [58,] 0.6715252 0.398853432
##  [59,] 0.9598613 0.579732500
##  [60,] 0.9866583 0.478656114
##  [61,] 0.6965793 0.554996235
##  [62,] 0.9099350 0.011872771
##  [63,] 1.1893832 0.052932544
##  [64,] 0.8065924 0.037377162
##  [65,] 0.6211899 0.209017899
##  [66,] 1.1924662 2.142298281
##  [67,] 0.8896188 0.691637710
##  [68,] 1.0697689 2.526468226
##  [69,] 0.7203978 0.284929607
##  [70,] 0.9441486 0.557131071
##  [71,] 1.3151380 0.487938400
##  [72,] 1.1057814 1.664899555
##  [73,] 0.9146033 0.536859300
##  [74,] 0.9319780 0.190398941
##  [75,] 1.2106192 0.837438303
##  [76,] 1.1911358 0.978712708
##  [77,] 1.2084799 4.956758656
##  [78,] 1.1446202 0.914794026
##  [79,] 1.0565477 0.036602766
##  [80,] 0.8465233 0.518850733
##  [81,] 0.6662023 1.979427279
##  [82,] 1.0050771 0.261110198
##  [83,] 0.8361145 1.110219250
##  [84,] 1.2027890 1.390873434
##  [85,] 0.9272135 0.838170545
##  [86,] 0.8650711 0.859708051
##  [87,] 1.0594924 0.155492565
##  [88,] 1.1930031 2.500053764
##  [89,] 1.0527148 2.521198081
##  [90,] 0.9489267 2.878026171
##  [91,] 1.4284284 3.091468649
##  [92,] 0.9937395 0.011367641
##  [93,] 1.1496126 0.169057463
##  [94,] 1.0793182 0.306957157
##  [95,] 0.7521775 1.355646468
##  [96,] 1.0922955 0.352446329
##  [97,] 1.2241404 0.004261807
##  [98,] 0.9272597 0.397611831
##  [99,] 0.9913063 0.460493756
## [100,] 0.7770799 0.134893892
## 
## $observedFstatRow
## [1] 20.49307
## 
## $observedFstatCol
## [1] 0.09226298
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0.8712871

The bicluster is unstable.

Calculating Partial Rankings for Top D1 League A

The next step is to calculate partial rankings based on the indicators and HEIs in the top league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR’s indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 6 shows the result of partial ranking in the case of the top league.

C<-biclust::bicluster(mtx,res,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 6** League A (D1) by iBBiG",digits = 2)

Table 6 League A (D1) by iBBiG

	T5	R5	I4	Overall_Score	Rank
USA_Johns Hopkins University	0.98	0.98	0.98	0.98	12
USA_Yale University	0.99	0.99	0.99	0.99	6
Japan_Tohoku University	0.91	0.91	0.85	0.22	78
USA_University of Pittsburgh	0.93	0.92	0.93	0.93	41
USA_Columbia University	0.99	0.98	0.98	0.99	9
USA_University of Chicago	0.98	0.99	0.99	0.25	56
USA_California Institute of Technology (Caltech)	0.99	0.99	0.99	0.99	7
USA_University of Pennsylvania	0.98	0.98	0.97	0.98	13
Russia_Lomonosov Moscow State University	0.95	0.94	0.90	0.23	69
USA_Stanford University	1.00	1.00	1.00	1.00	3
USA_University of California, San Diego	0.96	0.96	0.96	0.96	25
Japan_Osaka University	0.91	0.92	0.84	0.22	77
USA_Washington University in St. Louis	0.93	0.93	0.91	0.93	43
Japan_Tokyo Institute of Technology	0.93	0.92	0.91	0.92	45
USA_University of California, Los Angeles	0.99	0.99	0.99	0.25	55
USA_Princeton University	0.99	0.99	0.99	0.99	5
USA_University of Michigan	0.99	0.99	0.98	0.99	8
USA_University of Maryland, College Park	0.90	0.91	0.92	0.23	73
USA_Massachusetts Institute of Technology (MIT)	1.00	1.00	1.00	1.00	2
USA_New York University	0.96	0.97	0.97	0.97	20
Japan_Kyoto University	0.97	0.97	0.94	0.24	60
Sweden_Karolinska Institute	0.92	0.93	0.95	0.93	36
USA_Harvard University	1.00	1.00	1.00	1.00	1
USA_University of North Carolina	0.95	0.95	0.95	0.24	61
USA_Cornell University	0.97	0.97	0.98	0.98	15
USA_University of Wisconsin - Madison	0.97	0.97	0.97	0.97	21
Republic of Korea_Korea Advanced Institute of Science and Technology (KAIST)	0.93	0.95	0.90	0.23	71
UK_University College London	0.97	0.97	0.98	0.97	18
Japan_University of Tokyo	0.98	0.98	0.97	0.98	14
UK_University of Oxford	0.99	0.99	0.99	0.25	54
USA_Brown University	0.90	0.91	0.91	0.91	51
USA_University of Minnesota	0.94	0.95	0.94	0.95	31
UK_University of Cambridge	1.00	1.00	0.99	0.25	53
USA_University of Washington	0.97	0.97	0.96	0.97	19
Taiwan_National Taiwan University	0.91	0.91	0.85	0.89	52
Switzerland_Ecole Polytechnique Federale de Lausanne	0.94	0.95	0.95	0.24	63
Russia_Financial University under the Government of the Russian Federation	0.90	0.91	0.93	0.91	50
UK_Imperial College London	0.98	0.98	0.98	0.98	10
China_Peking University	0.95	0.95	0.93	0.24	66
USA_Boston University	0.91	0.90	0.93	0.91	49
USA_University of Southern California	0.93	0.93	0.93	0.93	39
UK_London School of Economics and Political Science	0.97	0.96	0.97	0.24	58
China_Tsinghua University	0.96	0.96	0.95	0.96	26
USA_University of California, Davis	0.94	0.95	0.95	0.95	30
USA_Ohio State University	0.94	0.94	0.94	0.24	67
UK_King`s College London	0.94	0.94	0.95	0.94	32
UK_University of Edinburgh	0.95	0.94	0.95	0.95	29
USA_Northwestern University	0.96	0.96	0.96	0.24	59
Canada_McGill University	0.95	0.94	0.96	0.95	28
Switzerland_ETH Zurich (Swiss Federal Institute of Technology)	0.98	0.98	0.98	0.98	11
France_Sorbonne University	0.91	0.90	0.91	0.23	75
USA_Carnegie Mellon University	0.96	0.96	0.97	0.96	24
USA_Indiana University	0.92	0.92	0.92	0.92	47
UK_University of Manchester	0.94	0.94	0.96	0.24	65
USA_University of California, Berkeley	0.99	0.99	0.99	0.99	4
USA_Pennsylvania State University	0.95	0.95	0.96	0.96	27
Singapore_Nanyang Technological University	0.94	0.94	0.92	0.23	70
USA_University of Florida	0.92	0.91	0.92	0.92	48
USA_Michigan State University	0.93	0.92	0.94	0.93	37
USA_Purdue University	0.95	0.95	0.96	0.24	62
Australia_Australian National University	0.91	0.93	0.94	0.93	40
Singapore_National University of Singapore	0.98	0.98	0.96	0.97	17
USA_University of Illinois at Urbana - Champaign	0.97	0.97	0.97	0.24	57
Hong Kong_University of Hong Kong	0.94	0.93	0.92	0.94	35
Canada_University of British Columbia	0.96	0.96	0.97	0.96	23
Republic of Korea_Sungkyunkwan University	0.96	0.96	0.92	0.24	64
Canada_University of Toronto	0.97	0.97	0.98	0.98	16
Australia_University of Sydney	0.93	0.93	0.95	0.94	33
Netherlands_Wageningen University and Research Center	0.90	0.91	0.93	0.23	72
USA_Texas A&M University	0.92	0.92	0.94	0.93	42
USA_Georgia Institute of Technology	0.96	0.96	0.97	0.97	22
USA_University of California, Santa Barbara	0.92	0.93	0.94	0.23	68
Australia_Monash University	0.91	0.91	0.94	0.92	46
Germany_Ludwig Maximilian University of Munich	0.93	0.93	0.93	0.93	38
Australia_University of Queensland Australia	0.90	0.90	0.92	0.23	74
Belgium_Katholieke Universiteit Leuven (KU Leuven)	0.92	0.92	0.92	0.93	44
Germany_Technical University of Munich	0.93	0.93	0.94	0.94	34
Germany_Humboldt University of Berlin	0.90	0.90	0.90	0.23	76

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a very weak positive relationship between the two rankings.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.2387612

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 60198, p-value = 0.03551
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.2387612

To sum up, only the median top league A (where the threshold is 0.5) satisfies all criteria, such as:

Significance: + Median A: yes + Q1 A: yes + D1 A: no

Stability + Median A: yes + Q1 A: yes + D1 A: no

High correlation of partial ranks + Median A: yes + Q1 A: no + D1 A: no

Recursive, Hierarchical Biclustering

Since, only the median league A satisfies all criteria, the hierarchical biclustering is performed based on the median league where the algorithm is looking for the next bicluster within the former bicluster. The iteration is performed until all criteria (significance, stability, high correlation) are satisfied.

The 1-3 iterations

res <- iBBiG(binaryMatrix=binarize(mtx,threshold = 0.5),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 3800.414 and 
##   398 Rows and  17 columns

#The first iteration

C<-biclust::bicluster(mtx,res,number=1)
B<-as.matrix(as.data.frame(C[[1]]))

for (i in 1:ncol(B)){ #Normalization (min-max)
  B[,i]<-normalize(B[,i])
}

res <- iBBiG(binaryMatrix=binarize(B,threshold = 0.5),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 3481.81 and 
##   372 Rows and  17 columns

#The second iteration

C<-biclust::bicluster(mtx,res,number=1)
B<-as.matrix(as.data.frame(C[[1]]))

for (i in 1:ncol(B)){ #Normalization (min-max)
  B[,i]<-normalize(B[,i])
}

res <- iBBiG(binaryMatrix=binarize(B,threshold = 0.5),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 3532.033 and 
##   368 Rows and  17 columns

#The third iteration

C<-biclust::bicluster(mtx,res,number=1)
B<-as.matrix(as.data.frame(C[[1]]))

for (i in 1:ncol(B)){ #Normalization (min-max)
  B[,i]<-normalize(B[,i])
}

res <- iBBiG(binaryMatrix=binarize(B,threshold = 0.5),nModules = 1,alpha=0.3,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(res)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 1853.171 and 
##   187 Rows and  17 columns

In the first three iteration, there is no change in the number of columns. Regarding the number of HEIs (rows), the iteration resulted in only a few changes.

Analyzing Hierarchical D1 League A

Calculating F-tests of the Hierarchical Top D1 League A Bicluster

In Table 7 the results of the row and column effects (F-tests) can be seen. Both the row and column effects are significant, so the top league bicluster is significant.

Obs.FStat <- NULL
for (i in c(1:res@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=res,number=i)
}
kable(Obs.FStat,caption = "**Table 7** The results of row and column effects for the top Hierarchical D1 league")

Table 7 The results of row and column effects for the top Hierarchical D1 league

Fstat PValue Row Effect 16.23195 0 Column Effect 35.39930 0 Tukey test 239.38499 0

To see the differences between those HEIs that are included in the top league and those that are not in the top league, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 15). (The horizontal axis of Fig. 15 shows the HEIs, the vertical axis shows the mentioned parameters on normalized (0-1) data of indicators.) On Fig. 15 the red line indicates those HEIs that are included in the top league, while the black line shows the remaining HEIs. The HEIs in the top league have higher means and medians, and have lower variances.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 15 Mean, median, variance and MAD for the hierarchical top league HEIs

One can do the same for the columns (indicators). Fig. 16 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. (The horizontal axis of Fig. 16 shows the indicators, the vertical axis shows the mentioned parameters on normalized (0-1) data of HEIs.) The red line indicates those indicators that are in the top league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=res,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 16 Mean, median, variance and MAD for the hierarchical top league indicators

Heat Maps of the Hiearchical Top D1 League A Bicluster

Fig. 17 depicts the heat map of the top league. The top league contains 187 HEIs and 17 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=res,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 9 Heat map of the top league

Fig. 18 shows the heat map of the results of iBBiG on normalized data. The top league can be seen in the upper left corner of Fig. 18 which is enlarged on Fig. 17.

drawHeatmap(x=mtx,bicResult=res,local=FALSE,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 10 Heat map of the output after applying iBBiG on normalized data

Checking the Stability of the Hiearchical Top D1 League A Bicluster

The next step is to check the stability of the top league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=res,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 1.0352616 1.1090097
##   [2,] 1.0451449 1.4141309
##   [3,] 0.9392428 1.4792050
##   [4,] 1.2634685 1.1100560
##   [5,] 1.0231151 1.0421020
##   [6,] 1.0847226 1.5719150
##   [7,] 1.0432838 0.3691549
##   [8,] 0.8992676 1.1949762
##   [9,] 1.0464296 0.7066555
##  [10,] 0.9267019 0.4450594
##  [11,] 0.9805835 0.8921770
##  [12,] 0.9395440 0.5940682
##  [13,] 0.9889977 1.5690807
##  [14,] 1.0181849 0.8467447
##  [15,] 0.8860887 1.0016626
##  [16,] 1.0359630 0.6558003
##  [17,] 1.0221861 0.7469964
##  [18,] 1.1113105 1.0971511
##  [19,] 0.8537862 1.7004155
##  [20,] 0.9550401 0.9693629
##  [21,] 1.0643178 1.4429729
##  [22,] 1.0003501 0.7544478
##  [23,] 1.0322008 1.4801927
##  [24,] 0.8787242 0.7876785
##  [25,] 0.9279165 0.6850943
##  [26,] 0.9614968 0.5437795
##  [27,] 1.1840184 1.4432831
##  [28,] 0.8944840 1.0200579
##  [29,] 0.9344124 0.6275461
##  [30,] 0.9559261 0.6713972
##  [31,] 1.0548140 0.5746892
##  [32,] 0.9469299 0.8849642
##  [33,] 1.1859000 1.5289077
##  [34,] 0.9686574 1.4367793
##  [35,] 1.0055197 0.6201958
##  [36,] 1.0357462 1.0314483
##  [37,] 1.1275938 1.4544429
##  [38,] 0.8172645 1.1354942
##  [39,] 0.7525771 0.7670560
##  [40,] 0.8881980 0.6727722
##  [41,] 0.9131016 0.9840246
##  [42,] 0.9504450 0.5235680
##  [43,] 1.0693939 0.9592236
##  [44,] 0.9224509 0.8527652
##  [45,] 0.9378781 0.4072921
##  [46,] 0.8964782 0.5329688
##  [47,] 1.0376503 1.0059494
##  [48,] 1.0364662 1.2430973
##  [49,] 1.2225909 0.7778143
##  [50,] 0.9853346 1.3553988
##  [51,] 0.9087345 1.1620795
##  [52,] 0.8921322 0.9097590
##  [53,] 0.9880957 0.6026624
##  [54,] 0.8336401 1.4652388
##  [55,] 0.9839696 0.9082082
##  [56,] 1.0408004 1.2433652
##  [57,] 1.0323003 0.7340211
##  [58,] 0.9983129 1.5828366
##  [59,] 1.1462906 1.4310083
##  [60,] 1.0248888 1.1230750
##  [61,] 0.8839752 1.3380522
##  [62,] 0.9781948 0.6805715
##  [63,] 0.9444864 1.0186331
##  [64,] 0.8373428 1.2189886
##  [65,] 1.1053585 0.6834890
##  [66,] 1.0310326 1.2022660
##  [67,] 1.2650614 0.9877361
##  [68,] 1.1238023 1.2788567
##  [69,] 1.2991627 1.0991222
##  [70,] 0.9219947 1.9703502
##  [71,] 0.9813965 0.9440943
##  [72,] 0.7911791 1.4585470
##  [73,] 1.0284847 0.7500634
##  [74,] 1.0372101 0.3695893
##  [75,] 1.0558077 0.7087960
##  [76,] 1.1282738 0.9728363
##  [77,] 0.9363364 0.9916596
##  [78,] 0.9831467 0.6574284
##  [79,] 1.0444222 0.6408557
##  [80,] 1.0992337 1.3122081
##  [81,] 0.9860110 1.4596217
##  [82,] 0.8631633 1.1188551
##  [83,] 0.8503261 0.9968137
##  [84,] 0.9486442 0.6117436
##  [85,] 1.1419115 1.0075837
##  [86,] 1.0713652 0.8693692
##  [87,] 1.0693472 1.6816240
##  [88,] 0.9760340 0.9351859
##  [89,] 1.0842879 0.6267402
##  [90,] 1.0787558 0.7432800
##  [91,] 1.0529024 1.1446179
##  [92,] 1.0539502 0.5883511
##  [93,] 0.9321106 1.5035859
##  [94,] 0.8933362 1.0833679
##  [95,] 1.3384201 1.2774232
##  [96,] 0.9820034 1.6726558
##  [97,] 0.9117498 0.6782731
##  [98,] 0.9005589 1.1012726
##  [99,] 1.0167566 0.6370828
## [100,] 0.8666983 1.1127337
## 
## $observedFstatRow
## [1] 16.23195
## 
## $observedFstatCol
## [1] 35.3993
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

Since the bootstrapPvalueCol and the bootstrapPvalueRow are lower than 0.01, the bicluster is stable both for rows and columns.

Calculating Partial Rankings for the Hiearchical Top D1 League A

The next step is to calculate partial rankings based on the indicators and HEIs in the top league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR’s indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 8 shows the result of partial ranking in the case of the top league.

C<-biclust::bicluster(mtx,res,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 8** League A by iBBiG",digits = 2)

Table 8 League A by iBBiG

	T1	T2	T3	T4	T5	R1	R2	R3	R4	R5	I1	I2	I3	I4	I5	F1	F2	F3	F4	F5	Overall_Score	Rank
Iraq_Al-Karkh University of Science	1.00	0.03	0.00	0.00	0.00	0.03	0.00	0.03	0.03	0.00	0.24	0.00	1.00	0.08	0.32	0.01	0.01	0.02	0.20	1.00	0.23	359
USA_University of Nebraska Medical Center	0.99	0.99	0.66	0.98	0.19	0.48	0.65	0.54	0.40	0.15	0.72	0.38	0.24	0.48	0.46	0.56	0.97	0.28	0.65	0.60	0.57	191
Iraq_Al-Qasim green university Iraq	0.99	0.67	0.00	0.00	0.00	0.06	0.00	0.14	0.07	0.00	0.00	0.00	0.99	0.08	0.26	0.09	0.63	0.13	0.09	0.12	0.19	374
Russia_European University at St. Petersburg	0.99	0.00	0.00	0.00	0.33	0.10	0.00	0.17	0.17	0.31	0.55	0.77	0.11	0.08	0.37	0.25	0.88	0.33	0.24	0.36	0.35	313
USA_Vanderbilt University	0.99	0.98	0.46	0.94	0.89	0.77	0.81	0.93	0.62	0.88	0.53	0.63	0.32	0.83	0.58	0.56	0.95	0.25	0.80	0.83	0.86	28
USA_Emory University	0.99	0.97	0.61	0.95	0.90	0.80	0.63	0.92	0.66	0.89	0.67	0.75	0.33	0.87	0.67	0.95	0.98	0.28	0.80	0.37	0.91	11
USA_Wake Forest University	0.98	0.97	0.49	0.92	0.53	0.70	0.80	0.89	0.53	0.31	0.23	0.38	0.23	0.64	0.37	0.74	0.96	0.40	0.67	0.42	0.70	119
Slovenia_University of Nova Gorica	0.98	0.99	0.32	0.93	0.46	0.73	0.20	0.68	0.68	0.51	0.86	0.97	0.97	0.43	0.82	0.08	0.42	0.85	0.41	0.92	0.75	85
USA_Johns Hopkins University	0.98	0.99	0.49	0.96	0.98	0.92	0.75	0.95	0.85	0.98	0.75	0.85	0.49	0.98	0.79	0.96	0.98	0.09	0.99	0.93	0.97	2
Japan_Yokohama City University	0.98	0.96	0.23	0.60	0.19	0.49	0.68	0.48	0.44	0.15	0.28	0.13	0.09	0.43	0.22	0.19	0.70	0.83	0.30	0.43	0.53	217
Sweden_Swedish University of Agricultural Sciences	0.98	0.93	0.34	0.65	0.66	0.76	0.59	0.74	0.78	0.63	0.00	0.22	0.94	0.75	0.48	0.53	0.92	0.20	0.91	0.98	0.76	81
Russia_Bauman Moscow State Technical University	0.98	0.98	0.28	0.78	0.79	0.08	0.10	0.05	0.09	0.76	0.46	0.41	0.05	0.68	0.40	0.17	0.64	0.03	0.62	0.94	0.54	209
USA_University of Rochester	0.97	0.95	0.48	0.82	0.76	0.79	0.58	0.89	0.66	0.79	0.71	0.91	0.45	0.82	0.74	0.97	0.98	0.25	0.82	0.27	0.81	44
USA_Yale University	0.97	0.98	0.71	0.97	0.99	0.95	0.61	0.96	0.90	0.99	0.78	0.76	0.48	0.99	0.77	0.98	0.99	0.43	0.87	0.34	0.88	21
Iraq_Hawler Medical University	0.97	0.92	0.03	0.05	0.00	0.00	0.06	0.00	0.00	0.00	0.19	0.11	0.00	0.08	0.08	0.44	0.87	0.00	0.29	0.18	0.19	371
Russia_Ufa State Aviation Technical University	0.97	0.94	0.04	0.06	0.24	0.09	0.04	0.24	0.08	0.31	0.03	0.09	0.51	0.43	0.26	0.03	0.10	0.98	0.01	0.01	0.32	323
Kazakhstan_L.N. Gumilyov Eurasian National University	0.97	0.89	0.08	0.15	0.43	0.11	0.23	0.20	0.08	0.25	0.60	0.17	0.94	0.24	0.49	0.04	0.13	0.27	0.07	0.39	0.42	269
USA_University of Miami	0.96	0.94	0.31	0.64	0.70	0.58	0.88	0.77	0.48	0.70	0.77	0.66	0.38	0.67	0.63	0.90	0.97	0.38	0.65	0.29	0.73	109
USA_Columbia University	0.96	0.99	0.68	0.99	0.99	0.84	0.93	0.97	0.68	0.98	0.81	0.96	0.51	0.98	0.84	0.89	0.96	0.25	0.83	0.62	0.90	13
USA_University of Chicago	0.96	0.97	0.71	0.96	0.98	0.99	0.56	0.99	0.93	0.99	0.81	0.83	0.50	0.99	0.80	0.96	0.98	0.56	0.83	0.38	0.89	15
China_Southern Medical University - China	0.96	0.93	0.44	0.77	0.24	0.39	0.87	0.37	0.37	0.00	0.11	0.31	0.08	0.08	0.13	0.30	0.72	0.34	0.56	0.70	0.50	230
Japan_University of Yamanashi	0.96	0.90	0.26	0.50	0.19	0.39	0.89	0.25	0.38	0.47	0.20	0.21	0.14	0.18	0.17	0.53	0.86	0.75	0.33	0.18	0.52	225
Denmark_Technical University of Denmark	0.96	0.94	0.61	0.88	0.79	0.82	0.55	0.80	0.76	0.82	0.96	0.84	0.91	0.84	0.91	0.56	0.87	0.18	0.91	0.99	0.83	36
Italy_Scuola Normale Superiore di Pisa	0.95	0.97	0.97	0.99	0.73	1.00	0.38	0.98	0.99	0.67	0.16	0.53	0.96	0.72	0.60	0.76	0.93	0.98	0.31	0.20	0.80	52
Saudi Arabia_King Fahd University of Petroleum and Minerals	0.95	0.94	0.15	0.38	0.70	0.47	0.47	0.46	0.50	0.68	0.99	0.59	0.79	0.26	0.67	0.85	0.94	0.63	0.50	0.18	0.68	130
Iran_Tehran University of Medical Sciences	0.95	0.99	0.92	1.00	0.72	0.45	0.29	0.34	0.53	0.61	0.04	0.36	0.11	0.64	0.28	0.96	0.98	0.64	0.52	0.12	0.69	124
Japan_Gifu University	0.95	0.89	0.31	0.56	0.29	0.36	0.88	0.16	0.44	0.20	0.55	0.24	0.16	0.48	0.35	0.21	0.54	0.86	0.28	0.36	0.46	248
Russia_Saint Petersburg State University	0.94	0.93	0.38	0.72	0.88	0.30	0.20	0.23	0.37	0.83	0.34	0.58	0.52	0.78	0.56	0.20	0.50	0.49	0.46	0.77	0.61	160
Japan_Osaka University	0.94	0.91	0.57	0.83	0.91	0.68	0.51	0.33	0.75	0.92	0.49	0.54	0.27	0.84	0.54	0.59	0.86	0.33	0.82	0.83	0.75	83
USA_Washington University in St. Louis	0.94	0.95	0.86	0.96	0.93	0.94	0.66	0.97	0.85	0.93	0.69	0.76	0.30	0.91	0.68	0.96	0.97	0.40	0.85	0.48	0.93	7
Japan_Tokyo Institute of Technology	0.94	0.95	0.62	0.92	0.93	0.76	0.54	0.35	0.85	0.92	0.52	0.60	0.37	0.91	0.61	0.43	0.78	0.35	0.86	0.96	0.79	59
Japan_Kumamoto University	0.93	0.87	0.31	0.53	0.33	0.41	0.70	0.25	0.44	0.47	0.25	0.36	0.22	0.56	0.34	0.59	0.85	0.60	0.47	0.32	0.52	224
Saudi Arabia_King Abdulaziz University	0.93	0.52	0.41	0.45	0.66	0.50	0.10	0.99	0.33	0.57	0.95	0.79	0.99	0.56	0.84	0.90	0.95	0.36	0.52	0.25	0.74	101
Japan_Okayama University	0.93	0.86	0.33	0.54	0.46	0.53	0.44	0.34	0.54	0.51	0.32	0.41	0.29	0.64	0.41	0.48	0.79	0.74	0.43	0.34	0.59	177
Russia_Tver State Technical University	0.93	0.71	0.19	0.28	0.09	0.10	0.14	0.06	0.10	0.00	0.00	0.67	0.48	0.08	0.30	0.06	0.15	0.22	0.11	0.27	0.29	339
United Arab Emirates_Khalifa University	0.93	0.95	0.16	0.40	0.13	0.63	0.99	0.54	0.65	0.20	1.00	0.88	0.97	0.28	0.79	0.26	0.56	0.99	0.07	0.05	0.73	107
Russia_National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)	0.92	0.97	0.47	0.89	0.72	0.65	0.59	0.65	0.68	0.69	0.74	0.82	0.65	0.43	0.67	0.47	0.78	0.23	0.85	0.90	0.77	74
Russia_Kursk State Medical University	0.92	0.97	0.35	0.79	0.00	0.06	0.55	0.11	0.05	0.00	0.04	0.96	0.19	0.08	0.31	0.06	0.14	0.20	0.06	0.09	0.28	341
France_Ecole Normale Superieure, Lyon	0.92	0.94	0.66	0.91	0.60	0.98	0.34	0.71	0.97	0.51	0.64	0.59	0.86	0.35	0.62	0.65	0.87	0.80	0.73	0.75	0.77	71
Belarus_Belarusian State University	0.91	0.54	0.08	0.09	0.40	0.23	0.08	0.89	0.14	0.31	0.49	0.46	0.98	0.43	0.60	0.09	0.19	0.15	0.27	0.78	0.39	291
USA_University of Michigan	0.91	0.86	0.69	0.85	0.99	0.85	0.62	0.89	0.78	0.99	0.74	0.71	0.38	0.98	0.72	0.83	0.92	0.35	0.82	0.68	0.86	30
Ukraine_National Technical University Kharkiv Polytechnic Institute	0.91	0.81	0.12	0.20	0.19	0.08	0.34	0.08	0.08	0.35	0.08	0.47	0.63	0.21	0.34	0.02	0.05	0.61	0.04	0.21	0.35	310
China_Guangzhou Medical University	0.90	0.96	0.12	0.35	0.00	0.40	0.55	0.43	0.37	0.00	0.52	0.10	0.12	0.08	0.19	0.14	0.30	0.81	0.27	0.61	0.36	303
Japan_Yamagata University	0.90	0.78	0.19	0.31	0.00	0.36	0.94	0.23	0.38	0.10	0.32	0.11	0.21	0.21	0.20	0.47	0.76	0.60	0.40	0.31	0.41	274
USA_University of Alaska	0.90	0.85	0.34	0.54	0.24	0.72	0.98	0.63	0.74	0.20	0.75	0.32	0.56	0.32	0.49	0.85	0.92	0.20	0.89	0.72	0.65	148
Japan_Osaka City University	0.89	0.80	0.38	0.57	0.24	0.41	0.72	0.22	0.47	0.25	0.43	0.21	0.20	0.38	0.30	0.67	0.85	0.76	0.38	0.18	0.49	236
Argentina_Austral University (Argentina)	0.89	0.96	0.05	0.14	0.19	0.14	0.73	0.31	0.11	0.35	0.32	0.38	0.57	0.48	0.44	0.14	0.29	0.88	0.05	0.04	0.39	286
USA_Rice University	0.89	0.86	0.68	0.84	0.85	0.90	0.58	0.98	0.79	0.84	0.79	0.88	0.59	0.86	0.80	0.88	0.93	0.50	0.75	0.49	0.92	8
Russia_Perm National Research Polytechnic University	0.88	0.75	0.13	0.20	0.09	0.09	0.13	0.03	0.13	0.10	0.06	0.39	0.04	0.08	0.13	0.15	0.30	0.04	0.59	0.94	0.30	330
Sweden_Karolinska Institute	0.88	0.88	0.80	0.92	0.92	0.99	0.57	0.91	0.98	0.93	0.72	0.77	0.95	0.95	0.87	0.84	0.91	0.32	0.97	1.00	1.00	1
Russia_Kazan National Research Technical University named after A.N. Tupolev	0.87	0.73	0.17	0.27	0.19	0.09	0.15	0.06	0.12	0.10	0.27	0.48	0.15	0.18	0.26	0.20	0.42	0.05	0.47	0.74	0.32	318
USA_University of Vermont	0.87	0.71	0.45	0.58	0.29	0.57	0.80	0.72	0.50	0.20	0.23	0.35	0.34	0.26	0.29	0.63	0.82	0.70	0.43	0.26	0.56	202
Taiwan_National Central University	0.87	0.88	0.31	0.56	0.36	0.40	0.31	0.35	0.39	0.31	0.56	0.50	0.48	0.38	0.48	0.29	0.54	0.15	0.73	1.00	0.60	173
India_Indian Institute of Science Education and Research, Pune	0.87	0.98	0.60	0.96	0.19	0.74	0.18	0.82	0.70	0.15	0.10	0.00	0.46	0.08	0.15	0.66	0.84	0.30	0.81	0.91	0.65	150
USA_Tufts University	0.87	0.93	0.93	0.97	0.74	0.84	0.93	0.93	0.75	0.72	0.53	0.58	0.47	0.78	0.60	0.85	0.91	0.51	0.72	0.51	0.81	48
India_Indian Institute of Science	0.86	0.99	0.97	1.00	0.84	0.94	0.48	0.28	0.99	0.85	0.07	0.08	0.25	0.80	0.30	0.91	0.93	0.37	0.97	0.86	0.73	110
Pakistan_Institute of Space Technology	0.86	0.92	0.00	0.00	0.00	0.03	0.00	0.00	0.01	0.00	0.00	0.00	1.00	0.08	0.26	0.18	0.35	0.01	0.13	0.17	0.24	353
Republic of Korea_Hallym University	0.86	0.59	0.13	0.16	0.00	0.44	0.36	0.15	0.60	0.00	0.26	0.27	0.05	0.08	0.15	0.34	0.60	0.84	0.37	0.41	0.39	292
Slovakia_Comenius University in Bratislava	0.85	0.91	0.38	0.68	0.43	0.35	0.64	0.45	0.31	0.20	0.26	0.61	0.87	0.38	0.54	0.13	0.24	0.55	0.37	0.81	0.55	206
USA_University of North Carolina	0.85	0.90	0.74	0.91	0.95	0.77	0.23	0.90	0.65	0.95	0.50	0.41	0.33	0.95	0.55	0.82	0.90	0.23	0.83	0.73	0.73	104
Russia_Magnitogorsk State Technical University	0.84	0.83	0.04	0.05	0.00	0.05	0.04	0.03	0.06	0.00	0.00	0.19	0.07	0.08	0.07	0.06	0.12	0.05	0.16	0.47	0.19	370
Sweden_University of Gothenburg	0.84	0.51	0.35	0.37	0.71	0.80	0.97	0.89	0.67	0.74	0.59	0.57	0.80	0.79	0.70	0.42	0.67	0.26	0.82	0.97	0.73	111
USA_Drexel University	0.84	0.64	0.76	0.79	0.60	0.56	0.82	0.81	0.42	0.57	0.64	0.73	0.29	0.66	0.59	0.60	0.80	0.64	0.42	0.29	0.72	112
USA_University of Wisconsin - Madison	0.84	0.75	0.80	0.85	0.97	0.73	0.84	0.87	0.64	0.97	0.59	0.58	0.38	0.97	0.64	0.74	0.87	0.25	0.81	0.80	0.89	14
USA_University of New Mexico	0.84	0.68	0.59	0.69	0.53	0.59	0.85	0.77	0.49	0.51	0.39	0.30	0.46	0.38	0.38	0.88	0.92	0.61	0.51	0.16	0.68	133
Tunisia_Universite de Tunis El Manar	0.83	0.89	0.62	0.84	0.19	0.22	0.08	0.16	0.24	0.20	0.32	0.10	0.77	0.53	0.43	0.02	0.04	0.79	0.19	0.88	0.39	287
Malaysia_Universiti Kebangsaan Malaysia	0.83	0.61	0.76	0.78	0.76	0.28	0.58	0.34	0.28	0.78	0.69	0.64	0.46	0.67	0.62	0.66	0.82	0.51	0.35	0.34	0.67	134
Thailand_Mahidol University	0.83	0.83	0.25	0.40	0.68	0.37	0.33	0.34	0.36	0.66	0.53	0.21	0.71	0.35	0.45	0.95	0.96	0.24	0.63	0.12	0.57	193
Republic of Korea_Korea Advanced Institute of Science and Technology (KAIST)	0.83	0.95	0.96	0.98	0.93	0.88	0.75	0.54	0.93	0.95	0.58	0.43	0.23	0.90	0.54	0.93	0.95	0.08	0.99	0.98	0.84	34
Ukraine_Kharkiv National University of Radio Electronics	0.83	0.58	0.14	0.17	0.13	0.07	0.13	0.21	0.05	0.31	0.04	0.47	0.59	0.08	0.29	0.03	0.05	0.43	0.04	0.10	0.32	325
Spain_University of Valladolid	0.83	1.00	0.17	0.99	0.09	0.26	0.12	0.25	0.24	0.15	0.29	0.28	0.47	0.48	0.38	0.15	0.24	0.91	0.12	0.19	0.45	253
UK_University College London	0.82	0.84	0.80	0.90	0.97	0.90	0.86	0.94	0.84	0.97	0.92	0.99	0.88	0.98	0.97	0.66	0.82	0.67	0.69	0.82	0.97	3
Russia_Altai State University	0.82	0.93	0.12	0.29	0.09	0.12	0.60	0.18	0.12	0.10	0.36	0.61	0.57	0.08	0.40	0.08	0.14	0.17	0.19	0.47	0.39	293
Russia_Far Eastern Federal University	0.82	0.77	0.16	0.25	0.13	0.17	0.11	0.11	0.20	0.31	0.62	0.74	0.33	0.21	0.47	0.37	0.60	0.35	0.30	0.24	0.43	259
Ukraine_Sumy State University	0.82	0.44	0.26	0.26	0.46	0.13	0.69	0.13	0.11	0.51	0.04	0.60	0.89	0.43	0.49	0.04	0.06	0.38	0.11	0.43	0.42	265
Spain_University of Zaragoza	0.82	0.77	0.67	0.80	0.36	0.42	0.83	0.43	0.36	0.40	0.13	0.33	0.57	0.43	0.36	0.15	0.25	0.89	0.22	0.41	0.57	194
USA_State University of New York, Stony Brook	0.82	0.70	0.63	0.72	0.68	0.60	0.59	0.82	0.50	0.74	0.78	0.81	0.55	0.75	0.73	0.63	0.80	0.56	0.53	0.41	0.71	117
Switzerland_USI - Universita della Svizzera italiana	0.81	0.87	0.45	0.71	0.00	0.94	0.94	0.86	0.93	0.31	0.99	1.00	0.94	0.24	0.81	0.42	0.66	0.89	0.54	0.74	0.78	63
Iraq_Mustansiriyah University	0.81	0.68	0.16	0.22	0.13	0.05	0.70	0.17	0.03	0.15	0.05	0.02	0.91	0.08	0.26	0.12	0.18	0.92	0.01	0.01	0.32	319
Malaysia_Universiti Sains Malaysia	0.81	0.76	0.77	0.85	0.82	0.40	0.44	0.29	0.46	0.81	0.61	0.63	0.58	0.56	0.60	0.52	0.72	0.80	0.34	0.20	0.66	145
Russia_Kazan Federal University	0.80	0.58	0.36	0.43	0.65	0.22	0.76	0.27	0.21	0.57	0.50	0.60	0.58	0.28	0.49	0.19	0.33	0.36	0.31	0.57	0.52	221
Spain_Polytechnic University of Catalonia	0.80	0.74	0.40	0.54	0.68	0.33	0.37	0.34	0.36	0.69	0.31	0.66	0.67	0.68	0.59	0.22	0.38	0.73	0.32	0.54	0.61	165
China_Jilin University	0.80	0.82	0.49	0.68	0.24	0.43	0.43	0.39	0.41	0.20	0.30	0.18	0.09	0.32	0.21	0.31	0.51	0.51	0.51	0.65	0.46	249
USA_Brown University	0.80	0.72	0.80	0.84	0.90	0.97	0.43	0.92	0.96	0.91	0.76	0.76	0.36	0.91	0.71	0.93	0.94	0.73	0.75	0.39	0.89	16
Lithuania_Vilnius University	0.80	0.79	0.25	0.39	0.40	0.35	0.50	0.48	0.30	0.31	0.61	0.45	0.71	0.43	0.55	0.13	0.20	0.40	0.43	0.91	0.47	246
Russia_Ural Federal University	0.79	0.40	0.17	0.16	0.58	0.21	0.13	0.09	0.25	0.40	0.72	0.47	0.30	0.43	0.48	0.17	0.30	0.29	0.42	0.78	0.43	262
China_Zhejiang University	0.79	0.77	0.90	0.92	0.80	0.92	0.48	0.55	0.95	0.78	0.72	0.72	0.23	0.70	0.60	0.98	0.98	0.06	0.99	0.88	0.86	26
Russia_Voronezh State University	0.79	0.63	0.21	0.27	0.19	0.13	0.19	0.07	0.16	0.31	0.23	0.48	0.19	0.43	0.33	0.07	0.12	0.66	0.12	0.31	0.32	321
USA_University of Washington	0.77	0.70	0.73	0.80	0.97	0.89	0.31	0.97	0.78	0.97	0.73	0.67	0.43	0.96	0.71	0.94	0.94	0.22	0.89	0.63	0.88	20
Taiwan_National Taiwan University	0.77	0.87	0.55	0.78	0.91	0.77	0.61	0.44	0.84	0.91	0.59	0.52	0.35	0.85	0.58	0.55	0.72	0.30	0.88	0.95	0.78	64
Russia_Moscow Institute of Physics and Technology	0.77	0.79	0.66	0.79	0.88	0.65	0.29	0.48	0.72	0.84	0.74	0.66	0.65	0.70	0.70	0.70	0.82	0.36	0.79	0.86	0.80	56
USA_Rutgers the State University of New Jersey	0.76	0.63	0.74	0.77	0.89	0.64	0.89	0.72	0.59	0.89	0.56	0.69	0.43	0.90	0.65	0.81	0.88	0.32	0.73	0.48	0.75	90
Colombia_Universidad Pontificia Bolivariana de Medellin-Colombia	0.76	0.95	0.05	0.12	0.24	0.13	0.15	0.30	0.10	0.60	0.16	0.09	0.84	0.60	0.42	0.25	0.41	0.12	0.20	0.18	0.39	288
Russia_National Research University of Electronic Technology (MIET)	0.76	0.60	0.19	0.24	0.29	0.12	0.12	0.04	0.17	0.31	0.23	0.24	0.21	0.56	0.31	0.41	0.60	0.04	0.79	0.91	0.39	290
Russia_Novosibirsk State Technical University	0.76	0.69	0.10	0.14	0.43	0.15	0.07	0.10	0.16	0.47	0.17	0.75	0.29	0.43	0.41	0.10	0.14	0.39	0.21	0.49	0.34	314
Russia_Moscow State University of Design and Technology (MSUDT)	0.75	0.55	0.09	0.11	0.09	0.04	0.26	0.01	0.10	0.00	0.13	0.40	0.02	0.21	0.18	0.07	0.11	0.59	0.07	0.10	0.23	360
Russia_Financial University under the Government of the Russian Federation	0.75	0.63	0.15	0.19	0.90	0.05	0.09	0.18	0.09	0.91	0.08	0.40	0.06	0.93	0.37	0.23	0.36	0.11	0.15	0.13	0.32	322
China_East China Normal University	0.75	0.83	0.55	0.75	0.40	0.45	0.45	0.48	0.43	0.40	0.73	0.68	0.33	0.48	0.56	0.63	0.77	0.17	0.74	0.71	0.60	171
Russia_Mordovia State University	0.75	0.60	0.12	0.15	0.29	0.09	0.13	0.08	0.09	0.51	0.09	0.52	0.05	0.43	0.26	0.10	0.14	0.12	0.14	0.28	0.26	348
Estonia_University of Tartu	0.74	0.76	0.50	0.65	0.63	0.59	0.00	0.75	0.48	0.57	0.47	0.42	0.90	0.60	0.60	0.38	0.56	0.50	0.56	0.86	0.58	185
USA_University of Iowa	0.74	0.60	0.78	0.79	0.86	0.62	0.65	0.77	0.55	0.85	0.66	0.56	0.35	0.84	0.61	0.92	0.93	0.30	0.73	0.38	0.74	94
Russia_Mendeleyev University of Chemical Technology	0.74	0.83	0.37	0.56	0.40	0.19	0.54	0.06	0.27	0.35	0.04	0.16	0.04	0.21	0.09	0.18	0.27	0.34	0.42	0.72	0.39	289
Russia_Bashkir State University	0.73	0.66	0.19	0.26	0.13	0.15	0.42	0.08	0.16	0.10	0.03	0.20	0.06	0.08	0.08	0.07	0.11	0.53	0.16	0.43	0.28	344
Russia_Volgograd State University	0.73	0.50	0.18	0.20	0.00	0.10	0.39	0.03	0.12	0.00	0.14	0.19	0.08	0.08	0.11	0.07	0.11	0.55	0.09	0.19	0.20	366
Hungary_University of Debrecen	0.73	0.90	0.20	0.40	0.19	0.32	0.29	0.55	0.26	0.00	0.43	0.72	0.72	0.18	0.51	0.41	0.58	0.52	0.33	0.26	0.45	252
UK_London School of Economics and Political Science	0.73	0.75	0.50	0.64	0.97	0.47	0.99	0.79	0.56	0.96	0.98	1.00	0.65	0.97	0.92	0.64	0.77	0.77	0.41	0.25	0.84	33
Russia_Tomsk State University	0.72	0.88	0.82	0.93	0.73	0.45	0.89	0.43	0.52	0.70	0.86	0.89	0.70	0.60	0.78	0.32	0.49	0.38	0.67	0.92	0.75	93
South Africa_University of Cape Town	0.72	0.71	0.40	0.53	0.78	0.71	0.38	0.80	0.68	0.77	0.82	0.71	0.95	0.75	0.82	0.58	0.72	0.43	0.73	0.71	0.77	72
USA_American University	0.72	0.75	0.86	0.90	0.46	0.33	0.45	0.98	0.25	0.31	0.40	0.57	0.17	0.48	0.40	0.65	0.78	0.75	0.22	0.07	0.60	174
Russia_Plekhanov Russian University of Economics	0.72	0.28	0.32	0.26	0.19	0.06	0.47	0.07	0.07	0.25	0.44	0.43	0.10	0.26	0.30	0.24	0.35	0.09	0.11	0.08	0.28	342
USA_University of California, Davis	0.72	0.49	0.67	0.63	0.94	0.78	0.69	0.82	0.71	0.95	0.76	0.62	0.50	0.95	0.72	0.93	0.93	0.29	0.83	0.49	0.82	41
Republic of Korea_Gwangju Institute of Science and Technology	0.71	0.98	0.94	0.99	0.19	0.93	0.19	0.41	0.98	0.40	0.44	0.31	0.40	0.08	0.30	0.95	0.94	0.21	0.99	0.87	0.76	79
Poland_Lodz University of Technology	0.71	0.74	0.13	0.20	0.13	0.26	0.17	0.16	0.32	0.15	0.15	0.22	0.22	0.08	0.16	0.19	0.27	0.81	0.25	0.34	0.32	324
Sweden_Lund University	0.71	0.91	0.53	0.80	0.88	0.85	0.78	0.81	0.82	0.88	0.72	0.73	0.91	0.87	0.83	0.48	0.63	0.24	0.90	0.98	0.86	27
Republic of Korea_Yonsei University	0.70	0.33	0.81	0.68	0.89	0.88	0.40	0.45	0.93	0.88	0.67	0.71	0.16	0.77	0.58	0.98	0.97	0.34	0.92	0.35	0.66	144
USA_Brandeis University	0.70	0.32	0.50	0.43	0.36	0.80	0.66	1.00	0.51	0.31	0.55	0.86	0.51	0.48	0.61	0.78	0.84	0.37	0.67	0.51	0.61	159
Taiwan_Chang Gung University	0.70	0.71	0.34	0.47	0.33	0.61	0.43	0.22	0.82	0.44	0.27	0.27	0.11	0.53	0.29	0.57	0.70	0.70	0.66	0.85	0.58	190
Russia_Northern (Arctic) Federal University (NArFU)	0.69	0.42	0.23	0.21	0.00	0.07	0.62	0.05	0.09	0.00	0.20	0.23	0.04	0.08	0.12	0.12	0.15	0.07	0.18	0.35	0.22	361
Azerbaijan_Baku State University	0.69	0.54	0.15	0.17	0.13	0.10	0.22	0.09	0.10	0.31	0.23	0.13	0.71	0.43	0.37	0.02	0.03	0.56	0.07	0.62	0.33	316
Thailand_Thammasat University	0.69	0.43	0.10	0.10	0.29	0.16	0.92	0.21	0.15	0.25	0.57	0.09	0.45	0.21	0.32	0.58	0.70	0.07	0.45	0.30	0.38	297
China_Renmin University of China	0.69	0.80	0.79	0.88	0.36	0.26	0.58	0.43	0.25	0.40	0.48	0.32	0.45	0.32	0.39	0.67	0.77	0.34	0.38	0.18	0.52	223
USA_Ohio State University	0.69	0.48	0.78	0.73	0.94	0.71	0.71	0.84	0.63	0.94	0.84	0.59	0.41	0.94	0.71	0.94	0.94	0.33	0.75	0.34	0.82	39
UK_Kings College London | 0.69| 0.61| 0.73| 0.76| 0.94| 0.86| 0.93| 0.96| 0.78| 0.94| 0.92| 0.97| 0.84| 0.95| 0.95| 0.61| 0.72| 0.74| 0.59| 0.67| 0.91| 12| |Hungary_University of Szeged | 0.68| 0.85| 0.32| 0.52| 0.29| 0.38| 0.38| 0.49| 0.34| 0.20| 0.39| 0.67| 0.64| 0.24| 0.49| 0.41| 0.57| 0.71| 0.31| 0.24| 0.47| 244| |Russia_Saint-Petersburg State Electotechnical University ``LETI`` | 0.68| 0.80| 0.20| 0.34| 0.49| 0.14| 0.46| 0.07| 0.17| 0.40| 0.05| 0.73| 0.23| 0.53| 0.38| 0.17| 0.23| 0.11| 0.42| 0.80| 0.43| 260| |Norway_University of Bergen | 0.68| 0.89| 0.51| 0.77| 0.65| 0.85| 0.49| 0.90| 0.79| 0.64| 0.80| 0.62| 0.94| 0.64| 0.77| 0.56| 0.68| 0.78| 0.56| 0.58| 0.77| 75| |Russia_Samara University | 0.68| 0.65| 0.09| 0.12| 0.19| 0.16| 0.09| 0.07| 0.16| 0.25| 0.05| 0.14| 0.21| 0.35| 0.18| 0.10| 0.13| 0.38| 0.21| 0.53| 0.26| 351| |UK_St Georges University of London	0.68	0.40	0.41	0.38	0.33	0.97	0.97	0.97	0.94	0.31	0.70	0.79	0.69	0.43	0.66	0.55	0.67	0.92	0.51	0.46	0.71	116
Austria_University of Innsbruck	0.68	0.76	0.56	0.72	0.46	0.60	0.20	0.75	0.49	0.40	0.93	0.97	0.96	0.38	0.83	0.33	0.46	0.66	0.46	0.66	0.73	105
USA_Worcester Polytechnic Institute	0.67	0.57	0.29	0.34	0.33	0.41	0.24	0.48	0.41	0.20	0.62	0.79	0.43	0.28	0.53	0.65	0.75	0.61	0.42	0.22	0.53	218
UK_University of Edinburgh	0.67	0.64	0.75	0.78	0.95	0.84	0.74	0.97	0.69	0.94	0.89	0.96	0.87	0.95	0.94	0.64	0.75	0.58	0.66	0.75	0.91	9
USA_Northwestern University	0.67	0.84	0.96	0.96	0.96	0.97	0.65	0.97	0.94	0.96	0.79	0.75	0.36	0.96	0.73	0.97	0.96	0.35	0.93	0.64	0.91	10
India_University of Hyderabad	0.67	0.94	0.90	0.96	0.51	0.47	0.35	0.22	0.57	0.40	0.00	0.06	0.11	0.21	0.08	0.04	0.05	0.91	0.28	0.97	0.49	238
Canada_University of Sherbrooke	0.66	0.63	0.75	0.78	0.13	0.37	0.51	0.45	0.33	0.25	0.77	0.38	0.50	0.28	0.48	0.46	0.59	0.60	0.37	0.48	0.59	180
USA_Temple University	0.66	0.55	0.85	0.81	0.66	0.49	0.99	0.79	0.41	0.68	0.32	0.46	0.37	0.76	0.48	0.59	0.69	0.31	0.63	0.50	0.62	158
Tunisia_Universite de la Manouba	0.65	0.72	0.24	0.35	0.00	0.17	0.04	0.16	0.17	0.00	0.14	0.07	0.83	0.08	0.27	0.05	0.07	0.98	0.03	0.03	0.35	308
China_Tongji University	0.65	0.85	0.64	0.82	0.72	0.61	0.40	0.48	0.72	0.73	0.86	0.59	0.26	0.64	0.60	0.70	0.77	0.13	0.95	0.95	0.72	113
Ukraine_South Ukrainian National Pedagogical University named after K.D. Ushynsky	0.65	0.41	0.33	0.32	0.13	0.05	0.09	0.07	0.06	0.25	0.18	0.28	0.96	0.24	0.41	0.03	0.03	0.48	0.04	0.12	0.30	334
China_Nankai University	0.64	0.75	0.78	0.84	0.33	0.66	0.52	0.76	0.61	0.35	0.65	0.36	0.12	0.38	0.38	0.55	0.66	0.50	0.66	0.61	0.63	153
China_Beijing Institute of Technology	0.64	0.82	0.60	0.76	0.53	0.52	0.27	0.52	0.56	0.51	0.12	0.41	0.13	0.72	0.34	0.73	0.79	0.07	0.97	0.97	0.58	188
Japan_Yokohama National University	0.64	0.64	0.35	0.43	0.43	0.30	0.91	0.21	0.32	0.40	0.51	0.35	0.17	0.38	0.35	0.26	0.35	0.18	0.64	0.87	0.51	229
Russia_Belgorod National Research University	0.64	0.31	0.30	0.25	0.19	0.15	0.15	0.32	0.14	0.15	0.21	0.72	0.52	0.08	0.38	0.14	0.16	0.08	0.35	0.73	0.31	327
China_Beijing Jiaotong University	0.63	0.75	0.37	0.52	0.40	0.39	0.24	0.41	0.43	0.40	0.28	0.37	0.28	0.53	0.36	0.41	0.53	0.24	0.69	0.77	0.49	237
France_Sorbonne University	0.63	0.81	0.87	0.92	0.91	0.91	0.53	0.80	0.88	0.90	0.57	0.75	0.88	0.91	0.79	0.27	0.35	0.97	0.24	0.40	0.78	67
UK_University of Southampton	0.63	0.49	0.74	0.70	0.80	0.91	1.00	0.95	0.81	0.83	0.88	0.93	0.87	0.87	0.91	0.52	0.62	0.83	0.52	0.59	0.84	31
USA_Carnegie Mellon University	0.63	0.83	0.69	0.82	0.96	0.88	0.66	0.91	0.82	0.96	0.83	0.99	0.55	0.97	0.86	0.92	0.91	0.16	0.95	0.75	0.95	4
USA_Indiana University	0.62	0.53	0.72	0.71	0.92	0.58	0.57	0.77	0.51	0.92	0.68	0.65	0.38	0.92	0.67	0.66	0.74	0.46	0.62	0.47	0.78	66
UK_University of Manchester	0.62	0.47	0.75	0.69	0.94	0.78	0.85	0.85	0.69	0.94	0.86	0.96	0.80	0.96	0.92	0.60	0.68	0.65	0.61	0.70	0.87	25
China_Jinan University	0.62	0.57	0.32	0.37	0.13	0.34	0.68	0.42	0.34	0.15	0.48	0.92	0.14	0.21	0.43	0.64	0.71	0.44	0.46	0.32	0.50	231
China_Beihang University	0.62	0.75	0.64	0.75	0.53	0.55	0.32	0.54	0.68	0.51	0.51	0.35	0.20	0.56	0.40	0.75	0.80	0.13	0.94	0.90	0.66	142
China_Shandong University	0.61	0.62	0.57	0.64	0.24	0.79	0.99	0.46	0.85	0.31	0.63	0.34	0.12	0.18	0.31	0.56	0.66	0.58	0.74	0.72	0.60	172
UK_University of Liverpool	0.61	0.30	0.56	0.47	0.78	0.79	0.60	0.86	0.72	0.78	0.85	0.92	0.90	0.85	0.90	0.50	0.59	0.81	0.49	0.53	0.76	80
India_Indian Institute of Technology, Kharagpur	0.61	0.96	0.81	0.96	0.71	0.75	0.18	0.31	0.00	0.72	0.52	0.04	0.00	0.60	0.28	0.58	0.66	0.00	0.74	0.78	0.58	189
USA_Northeastern University	0.61	0.47	0.84	0.77	0.55	0.69	0.74	0.91	0.57	0.54	0.75	0.94	0.57	0.64	0.74	0.79	0.82	0.59	0.57	0.29	0.72	114
Spain_Polytechnic University of Madrid	0.60	0.57	0.35	0.40	0.70	0.30	0.22	0.35	0.31	0.64	0.17	0.61	0.54	0.53	0.46	0.18	0.21	0.72	0.29	0.56	0.48	239
UK_University of Bristol	0.60	0.39	0.75	0.66	0.86	0.92	0.86	0.96	0.81	0.86	0.84	0.83	0.73	0.89	0.84	0.63	0.69	0.73	0.62	0.69	0.82	38
China_Wuhan University of Technology	0.60	0.50	0.17	0.18	0.33	0.29	0.21	0.86	0.23	0.57	0.21	0.18	0.30	0.48	0.29	0.45	0.54	0.22	0.41	0.46	0.37	298
Poland_University of Warsaw	0.59	0.88	0.27	0.49	0.65	0.39	0.43	0.63	0.30	0.60	0.42	0.50	0.70	0.60	0.56	0.26	0.32	0.23	0.55	0.79	0.58	187
USA_Florida Institute of Technology	0.59	0.66	0.48	0.58	0.19	0.63	0.56	0.96	0.46	0.15	0.47	0.92	0.92	0.43	0.70	0.55	0.62	0.86	0.29	0.14	0.57	192
USA_University of Utah	0.58	0.55	0.77	0.76	0.79	0.77	0.95	0.77	0.70	0.81	0.31	0.43	0.31	0.81	0.47	0.96	0.94	0.43	0.74	0.28	0.73	108
Russia_Samara State Technical University	0.58	0.57	0.11	0.14	0.13	0.11	0.15	0.06	0.12	0.15	0.05	0.12	0.02	0.24	0.09	0.13	0.14	0.10	0.26	0.58	0.24	357
Iraq_University of Babylon	0.58	0.31	0.19	0.16	0.09	0.08	0.20	0.37	0.05	0.10	0.03	0.02	0.97	0.08	0.27	0.16	0.17	0.08	0.08	0.17	0.20	369
UK_Newcastle University	0.58	0.43	0.64	0.57	0.69	0.67	0.73	0.84	0.62	0.67	0.83	0.88	0.75	0.79	0.83	0.49	0.56	0.59	0.62	0.77	0.75	87
China_Northwest University, Xi’an	0.57	0.61	0.30	0.37	0.53	0.38	0.33	0.47	0.34	0.35	0.12	0.19	0.10	0.67	0.26	0.27	0.33	0.63	0.36	0.57	0.44	256
UK_University of Dundee	0.57	0.51	0.48	0.50	0.61	0.67	0.83	0.94	0.49	0.51	0.76	0.78	0.71	0.69	0.75	0.48	0.56	0.47	0.60	0.79	0.70	120
Macau_University of Macau	0.57	0.62	0.53	0.60	0.24	0.54	0.28	0.67	0.62	0.35	1.00	0.94	0.39	0.43	0.70	0.84	0.83	0.52	0.66	0.40	0.65	149
Spain_University of Navarra	0.57	0.68	0.51	0.62	0.70	0.62	0.27	0.69	0.58	0.61	0.60	0.77	0.56	0.64	0.65	0.68	0.73	0.60	0.56	0.45	0.70	121
USA_East Carolina University	0.57	0.45	0.39	0.39	0.13	0.28	0.51	0.38	0.27	0.15	0.59	0.12	0.21	0.24	0.28	0.59	0.65	0.64	0.27	0.11	0.40	284
China_Northeastern University (China)	0.56	0.67	0.45	0.55	0.13	0.34	0.34	0.39	0.44	0.40	0.79	0.24	0.12	0.53	0.42	0.58	0.65	0.11	0.86	0.87	0.51	227
China_Xiamen University	0.56	0.78	0.40	0.56	0.40	0.49	0.19	0.58	0.43	0.35	0.36	0.25	0.32	0.26	0.29	0.62	0.67	0.27	0.67	0.69	0.56	199
Spain_University of the Basque Country	0.55	0.64	0.54	0.62	0.29	0.49	0.86	0.49	0.45	0.25	0.09	0.25	0.68	0.35	0.34	0.24	0.28	0.87	0.27	0.34	0.48	240
Russia_Tver State University	0.55	1.00	0.03	0.27	0.09	0.11	0.73	0.05	0.13	0.10	0.06	0.16	0.20	0.08	0.11	0.06	0.07	0.03	0.67	1.00	0.36	305
Republic of Korea_Yeungnam University	0.54	0.25	0.30	0.23	0.19	0.44	0.28	0.38	0.50	0.20	0.56	0.29	0.27	0.30	0.35	0.36	0.43	0.74	0.41	0.46	0.43	264
Russia_Tomsk State University of Control Systems and Radioelectronics (TUSUR University)	0.54	0.59	0.21	0.26	0.19	0.15	0.17	0.27	0.15	0.31	0.23	0.77	0.32	0.28	0.40	0.22	0.24	0.05	0.58	0.89	0.37	300
UK_University of Sheffield	0.54	0.38	0.79	0.70	0.87	0.72	0.85	0.87	0.64	0.87	0.83	0.92	0.72	0.91	0.87	0.57	0.62	0.64	0.59	0.68	0.80	53
Taiwan_National Chung Cheng University	0.54	0.56	0.26	0.32	0.19	0.29	0.25	0.15	0.38	0.31	0.15	0.26	0.13	0.32	0.20	0.18	0.19	0.33	0.57	0.88	0.37	299
UK_University of Birmingham	0.54	0.41	0.74	0.65	0.85	0.81	0.93	0.92	0.69	0.84	0.85	0.88	0.76	0.88	0.86	0.52	0.58	0.78	0.50	0.57	0.80	55
Spain_University of Valencia	0.54	0.63	0.56	0.63	0.49	0.52	0.25	0.72	0.41	0.64	0.16	0.56	0.67	0.67	0.52	0.19	0.21	0.91	0.22	0.35	0.54	210
Russia_Volgograd State Technical University	0.54	0.50	0.09	0.10	0.00	0.09	0.16	0.02	0.11	0.00	0.03	0.36	0.03	0.08	0.11	0.10	0.11	0.11	0.25	0.58	0.19	372
Chile_Pontificia University Catolica de Chile	0.53	0.81	0.18	0.32	0.74	0.53	0.16	0.52	0.50	0.68	0.60	0.37	0.90	0.69	0.65	0.47	0.53	0.31	0.69	0.75	0.56	195
India_Indian Institute of Technology, Kanpur	0.53	0.75	0.79	0.85	0.77	0.43	0.31	0.25	0.51	0.74	0.11	0.04	0.19	0.70	0.26	0.66	0.69	0.42	0.65	0.85	0.61	164
France_University Paris Diderot - Paris 7	0.52	0.81	1.00	0.99	0.00	0.93	0.73	0.97	0.80	0.51	0.66	0.76	0.86	0.38	0.67	0.21	0.23	0.99	0.04	0.02	0.67	139
Japan_University of Electro-Communications	0.52	0.57	0.39	0.46	0.24	0.42	0.56	0.19	0.55	0.31	0.49	0.30	0.41	0.32	0.38	0.36	0.43	0.71	0.48	0.56	0.47	242
Spain_ESIC Business and Marketing School	0.52	0.69	0.00	0.00	0.00	0.04	0.00	0.10	0.04	0.00	0.73	0.58	0.29	0.08	0.42	0.28	0.33	0.11	0.06	0.04	0.21	365
UK_University of York	0.52	0.31	0.72	0.59	0.72	0.81	0.80	0.83	0.75	0.75	0.82	0.81	0.63	0.81	0.79	0.54	0.59	0.79	0.53	0.57	0.77	76
Taiwan_National Chung Hsing University	0.52	0.63	0.38	0.48	0.40	0.36	0.62	0.20	0.41	0.57	0.33	0.27	0.12	0.48	0.29	0.36	0.42	0.36	0.60	0.87	0.48	241
UK_Swansea University	0.52	0.28	0.37	0.31	0.40	0.53	0.36	0.86	0.45	0.40	0.81	0.79	0.77	0.53	0.74	0.42	0.48	0.69	0.41	0.45	0.61	162
UK_Royal Holloway, University of London	0.51	0.30	0.72	0.57	0.61	0.69	0.88	0.97	0.58	0.63	0.93	0.94	0.91	0.73	0.90	0.43	0.49	0.90	0.30	0.22	0.75	91
UK_University of Reading	0.51	0.37	0.67	0.58	0.84	0.64	0.89	0.83	0.59	0.81	0.88	0.90	0.80	0.88	0.89	0.50	0.55	0.82	0.39	0.36	0.77	73
UK_University of Aberdeen	0.51	0.60	0.66	0.69	0.58	0.84	0.59	0.94	0.79	0.57	0.90	0.96	0.88	0.72	0.88	0.45	0.51	0.76	0.58	0.72	0.79	61
Azerbaijan_Azerbaijan University of Architecture and Construction	0.51	0.36	0.17	0.15	0.00	0.02	0.73	0.03	0.03	0.10	0.24	0.43	0.44	0.08	0.29	0.05	0.06	0.20	0.03	0.03	0.20	367
Thailand_Chiang Mai University	0.51	0.50	0.22	0.23	0.55	0.24	0.26	0.18	0.26	0.35	0.19	0.12	0.55	0.30	0.28	0.74	0.76	0.14	0.63	0.35	0.43	263
China_Nanjing University	0.50	0.86	0.84	0.92	0.72	0.85	0.29	0.65	0.87	0.71	0.98	0.49	0.26	0.69	0.61	0.80	0.80	0.31	0.90	0.84	0.82	37
India_Indian Institute of Technology, Madras	0.50	0.87	0.88	0.93	0.82	0.40	0.24	0.29	0.48	0.80	0.19	0.08	0.20	0.75	0.30	0.87	0.84	0.25	0.71	0.76	0.60	169
China_Nanjing University of Aeronautics & Astronautics	0.50	0.57	0.39	0.46	0.19	0.42	0.25	0.47	0.49	0.25	0.28	0.18	0.09	0.21	0.17	0.49	0.54	0.13	0.85	0.92	0.43	261
Switzerland_University of Geneva	0.50	0.83	0.73	0.84	0.78	0.95	0.21	0.92	0.91	0.77	0.95	0.97	0.96	0.79	0.94	0.62	0.65	0.75	0.68	0.76	0.87	22
Nigeria_University of Ibadan	0.49	0.77	0.60	0.74	0.61	0.25	0.56	0.61	0.21	0.51	0.51	0.09	0.60	0.32	0.38	0.11	0.11	0.78	0.15	0.31	0.54	207
Turkey_Koc University	0.49	0.47	0.32	0.33	0.67	0.43	0.17	0.31	0.57	0.71	0.62	0.32	0.51	0.74	0.55	0.97	0.93	0.21	0.80	0.31	0.58	184
China_Dalian University of Technology	0.49	0.59	0.51	0.57	0.36	0.55	0.36	0.49	0.60	0.44	0.60	0.14	0.16	0.48	0.34	0.44	0.49	0.29	0.76	0.89	0.56	201
China_China Pharmaceutical University	0.49	0.51	0.42	0.45	0.36	0.34	0.50	0.39	0.32	0.25	0.10	0.13	0.04	0.26	0.12	0.40	0.44	0.65	0.34	0.53	0.40	278
USA_Syracuse University	0.49	0.43	0.65	0.60	0.80	0.54	0.49	0.93	0.41	0.76	0.42	0.75	0.46	0.80	0.62	0.82	0.81	0.53	0.50	0.17	0.67	138
Republic of Korea_Hanyang University	0.49	0.37	0.91	0.79	0.69	0.81	0.77	0.41	0.93	0.68	0.82	0.77	0.25	0.32	0.55	0.92	0.90	0.14	0.98	0.81	0.74	98
USA_Boston College	0.48	0.42	0.39	0.38	0.80	0.50	0.50	0.67	0.48	0.80	0.65	0.54	0.22	0.84	0.57	0.94	0.91	0.67	0.44	0.08	0.68	128
USA_Oklahoma State University	0.48	0.31	0.55	0.46	0.36	0.56	0.88	0.67	0.53	0.25	0.70	0.39	0.42	0.26	0.44	0.70	0.71	0.69	0.48	0.21	0.56	197
Singapore_Nanyang Technological University	0.48	0.19	0.83	0.61	0.94	0.93	0.84	0.96	0.89	0.94	0.97	0.86	0.92	0.92	0.94	0.93	0.91	0.27	0.92	0.72	0.94	5
Norway_Norwegian University of Science and Technology	0.48	0.72	0.43	0.57	0.76	0.53	0.42	0.53	0.54	0.78	0.71	0.42	0.74	0.80	0.68	0.54	0.56	0.50	0.61	0.61	0.66	140
Taiwan_National Taipei University of Technology	0.48	0.46	0.35	0.35	0.36	0.33	0.26	0.25	0.37	0.54	0.46	0.42	0.09	0.48	0.36	0.57	0.59	0.14	0.73	0.89	0.49	232
Russia_Omsk State Technical University	0.48	0.56	0.17	0.19	0.09	0.07	0.75	0.06	0.09	0.00	0.04	0.74	0.10	0.18	0.26	0.07	0.07	0.09	0.16	0.41	0.25	352
UK_University of Portsmouth	0.47	0.22	0.21	0.15	0.13	0.45	0.49	0.88	0.31	0.20	0.84	0.83	0.91	0.24	0.71	0.28	0.30	0.95	0.12	0.07	0.53	215
China_Chongqing University	0.47	0.56	0.47	0.51	0.13	0.44	0.44	0.46	0.49	0.10	0.35	0.22	0.17	0.21	0.23	0.45	0.48	0.45	0.61	0.62	0.45	255
Turkey_Ege University	0.47	0.74	0.19	0.30	0.00	0.26	0.30	0.16	0.23	0.00	0.22	0.18	0.14	0.08	0.14	0.40	0.43	0.49	0.28	0.33	0.30	333
UK_University of Central Lancashire	0.47	0.22	0.14	0.11	0.19	0.28	0.27	0.43	0.25	0.31	0.65	0.70	0.65	0.56	0.65	0.29	0.32	0.93	0.11	0.07	0.40	279
Spain_University of Vigo	0.47	0.58	0.30	0.35	0.36	0.34	0.11	0.39	0.35	0.20	0.14	0.27	0.62	0.56	0.40	0.25	0.26	0.86	0.24	0.38	0.42	268
UK_Aberystwyth University	0.46	0.20	0.51	0.36	0.43	0.53	0.95	0.72	0.47	0.31	0.75	0.71	0.85	0.60	0.74	0.48	0.51	0.61	0.49	0.52	0.62	156
USA_Oregon State University	0.46	0.29	0.59	0.48	0.74	0.68	0.31	0.66	0.63	0.74	0.74	0.53	0.39	0.79	0.62	0.75	0.75	0.41	0.72	0.63	0.61	161
Japan_Kyushu Institute of Technology	0.46	0.44	0.41	0.40	0.46	0.46	0.81	0.28	0.54	0.31	0.46	0.22	0.32	0.60	0.40	0.33	0.38	0.80	0.39	0.40	0.53	220
New Zealand_Massey University	0.46	0.58	0.49	0.53	0.51	0.48	0.86	0.47	0.51	0.51	0.94	0.91	0.82	0.62	0.84	0.35	0.40	0.79	0.37	0.39	0.69	127
Canada_University of Calgary	0.45	0.44	0.77	0.70	0.75	0.83	0.88	0.72	0.83	0.75	0.80	0.75	0.65	0.83	0.77	0.68	0.68	0.52	0.77	0.74	0.80	54
Iraq_University of Diyala	0.45	0.45	0.14	0.14	0.00	0.06	0.42	0.30	0.04	0.00	0.00	0.00	0.98	0.08	0.26	0.02	0.02	0.58	0.03	0.17	0.22	362
China_University of Electronic Science and Technology of China	0.45	0.52	0.40	0.44	0.00	0.48	0.24	0.54	0.59	0.15	0.26	0.16	0.31	0.18	0.22	0.45	0.47	0.26	0.77	0.89	0.41	276
USA_University of Colorado	0.45	0.37	0.68	0.59	0.89	0.71	0.81	0.96	0.53	0.90	0.60	0.54	0.49	0.90	0.65	0.78	0.76	0.29	0.72	0.76	0.74	95
Czech Republic_University of West Bohemia	0.44	0.68	0.25	0.34	0.24	0.19	0.16	0.12	0.23	0.15	0.36	0.23	0.69	0.43	0.43	0.26	0.26	0.10	0.62	0.91	0.33	317
Switzerland_University of Bern	0.44	0.54	0.98	0.94	0.70	0.98	0.61	0.90	0.98	0.73	0.96	0.67	0.95	0.67	0.83	0.88	0.85	0.78	0.78	0.64	0.84	32
USA_University of California, Irvine	0.44	0.23	0.70	0.51	0.82	0.82	0.48	0.92	0.70	0.86	0.77	0.86	0.49	0.86	0.76	0.94	0.90	0.41	0.76	0.39	0.82	42
Finland_University of Helsinki	0.43	0.65	0.79	0.81	0.83	0.95	0.96	0.92	0.89	0.85	0.53	0.31	0.87	0.86	0.65	0.62	0.61	0.42	0.87	0.98	0.81	50
China_Sun Yat-sen University	0.43	0.53	0.75	0.73	0.58	0.63	0.43	0.59	0.65	0.60	0.41	0.45	0.22	0.56	0.41	0.98	0.95	0.26	0.81	0.30	0.68	129
USA_Colorado School of Mines	0.43	0.38	0.68	0.59	0.80	0.82	0.42	0.85	0.77	0.77	0.44	0.54	0.47	0.86	0.59	0.75	0.74	0.59	0.69	0.56	0.75	84
Portugal_Aveiro University	0.43	0.59	0.66	0.68	0.49	0.79	0.15	0.42	0.89	0.47	0.36	0.55	0.77	0.32	0.50	0.26	0.25	0.91	0.44	0.77	0.59	183
UK_University of Exeter	0.42	0.21	0.63	0.46	0.70	0.73	0.98	0.92	0.64	0.73	0.89	0.86	0.81	0.80	0.86	0.50	0.51	0.77	0.47	0.53	0.75	82
Romania_George Emil Palade University of Medicine, Pharmacy, Science, and Technology of Targu Mures	0.42	0.59	0.17	0.21	0.00	0.17	0.27	0.12	0.16	0.00	0.11	0.35	0.25	0.08	0.18	0.14	0.13	0.97	0.04	0.06	0.24	356
China_Ningbo University	0.41	0.55	0.05	0.06	0.00	0.39	0.17	0.40	0.39	0.00	0.25	0.30	0.07	0.08	0.16	0.34	0.37	0.57	0.42	0.45	0.30	329
India_Indian Institute of Technology, Delhi	0.41	0.78	0.91	0.93	0.84	0.57	0.18	0.30	0.77	0.81	0.18	0.08	0.13	0.73	0.27	0.90	0.86	0.46	0.76	0.61	0.62	157
UK_Queens University Belfast | 0.41| 0.24| 0.73| 0.54| 0.49| 0.70| 0.79| 0.76| 0.65| 0.57| 0.92| 0.94| 0.93| 0.72| 0.89| 0.49| 0.50| 0.68| 0.56| 0.65| 0.75| 88| |Russia_Moscow State Institute of Radio Engineering, Electrical & Automation | 0.40| 0.44| 0.07| 0.07| 0.74| 0.14| 0.05| 0.06| 0.17| 0.73| 0.07| 0.16| 0.09| 0.70| 0.25| 0.21| 0.18| 0.10| 0.44| 0.73| 0.28| 343| |Republic of Korea_Sejong University | 0.40| 0.27| 0.45| 0.36| 0.33| 0.52| 0.89| 0.54| 0.56| 0.20| 0.54| 0.50| 0.36| 0.43| 0.46| 0.34| 0.37| 0.38| 0.70| 0.84| 0.56| 198| |USA_University of Nebraska | 0.40| 0.44| 0.67| 0.62| 0.72| 0.65| 0.43| 0.74| 0.64| 0.66| 0.77| 0.54| 0.48| 0.67| 0.62| 0.78| 0.76| 0.37| 0.74| 0.57| 0.66| 143| |Russia_South Ural State University | 0.40| 0.37| 0.09| 0.09| 0.19| 0.11| 0.08| 0.11| 0.11| 0.15| 0.11| 0.30| 0.22| 0.18| 0.19| 0.11| 0.09| 0.10| 0.23| 0.54| 0.21| 364| |Japan_Hitotsubashi University | 0.39| 0.48| 0.45| 0.46| 0.51| 0.16| 0.21| 0.20| 0.20| 0.57| 0.53| 0.57| 0.44| 0.43| 0.49| 0.33| 0.36| 0.16| 0.40| 0.41| 0.42| 266| |Iraq_University of Thi-Qar | 0.39| 0.51| 0.09| 0.10| 0.00| 0.10| 0.12| 0.24| 0.06| 0.00| 0.00| 0.00| 0.96| 0.08| 0.25| 0.12| 0.10| 0.06| 0.12| 0.33| 0.17| 377| |Iraq_University College in Baghdad Iraq | 0.39| 0.05| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.08| 0.00| 0.10| 0.09| 0.00| 0.07| 0.12| 0.04| 391| |Qatar_University of Qatar | 0.39| 0.34| 0.03| 0.04| 0.46| 0.37| 0.05| 0.55| 0.40| 0.44| 1.00| 0.96| 0.99| 0.48| 0.88| 0.91| 0.87| 0.08| 0.88| 0.55| 0.53| 219| |USA_University of Oregon | 0.38| 0.21| 0.59| 0.43| 0.70| 0.56| 0.19| 0.95| 0.41| 0.74| 0.26| 0.57| 0.43| 0.76| 0.51| 0.77| 0.73| 0.41| 0.57| 0.35| 0.61| 167| |Canada_Laval University | 0.38| 0.39| 0.95| 0.86| 0.60| 0.72| 0.52| 0.62| 0.72| 0.61| 0.81| 0.61| 0.57| 0.76| 0.70| 0.57| 0.56| 0.37| 0.79| 0.83| 0.70| 118| |Republic of Korea_Kyung Hee University | 0.38| 0.53| 0.71| 0.69| 0.46| 0.80| 0.30| 0.39| 0.92| 0.47| 0.79| 0.79| 0.24| 0.43| 0.57| 0.92| 0.88| 0.32| 0.91| 0.56| 0.66| 147| |Romania_University of Bucharest | 0.37| 0.40| 0.43| 0.41| 0.61| 0.25| 0.39| 0.18| 0.28| 0.44| 0.14| 0.13| 0.49| 0.48| 0.30| 0.11| 0.09| 0.86| 0.19| 0.43| 0.36| 304| |Spain_University of Salamanca | 0.37| 0.48| 0.58| 0.56| 0.53| 0.41| 0.24| 0.47| 0.34| 0.44| 0.18| 0.67| 0.55| 0.35| 0.44| 0.20| 0.17| 0.85| 0.23| 0.34| 0.47| 245| |USA_State University of New York, Albany | 0.37| 0.30| 0.48| 0.39| 0.57| 0.58| 0.42| 0.90| 0.45| 0.70| 0.00| 0.49| 0.45| 0.64| 0.39| 0.60| 0.57| 0.47| 0.56| 0.58| 0.60| 168| |France_Universite Grenoble Alpes (UGA) | 0.36| 0.35| 0.82| 0.70| 0.64| 0.89| 0.70| 0.63| 0.88| 0.68| 0.55| 0.58| 0.88| 0.67| 0.68| 0.32| 0.32| 0.97| 0.29| 0.24| 0.67| 135| |Australia_Australian National University | 0.36| 0.44| 0.86| 0.77| 0.91| 0.94| 0.94| 0.89| 0.95| 0.93| 0.97| 0.98| 0.85| 0.94| 0.96| 0.82| 0.77| 0.37| 0.93| 0.90| 0.93| 6| |Singapore_National University of Singapore | 0.36| 0.24| 0.85| 0.65| 0.98| 0.89| 0.72| 0.82| 0.87| 0.98| 0.98| 0.88| 0.92| 0.96| 0.96| 0.97| 0.93| 0.24| 0.92| 0.68| 0.87| 23| |India_Vellore Institute of Technology | 0.36| 0.53| 0.39| 0.44| 0.19| 0.25| 0.10| 0.25| 0.00| 0.15| 0.56| 0.15| 0.00| 0.08| 0.19| 0.35| 0.34| 0.00| 0.14| 0.11| 0.30| 336| |USA_University of Illinois at Urbana - Champaign | 0.35| 0.33| 0.70| 0.57| 0.97| 0.91| 0.39| 0.87| 0.86| 0.97| 0.44| 0.82| 0.45| 0.97| 0.68| 0.89| 0.83| 0.44| 0.84| 0.58| 0.75| 92| |Taiwan_National Tsing Hua University | 0.35| 0.51| 0.61| 0.61| 0.75| 0.83| 0.36| 0.52| 0.85| 0.77| 0.37| 0.48| 0.37| 0.43| 0.41| 0.64| 0.59| 0.22| 0.93| 0.95| 0.66| 141| |New Zealand_University of Canterbury | 0.35| 0.41| 0.62| 0.56| 0.53| 0.69| 0.95| 0.72| 0.65| 0.60| 0.95| 0.82| 0.95| 0.69| 0.87| 0.36| 0.35| 0.77| 0.48| 0.53| 0.74| 99| |Romania_West University of Timisoara | 0.35| 0.11| 0.29| 0.17| 0.19| 0.40| 0.17| 0.87| 0.26| 0.15| 0.09| 0.24| 0.74| 0.08| 0.28| 0.11| 0.08| 0.95| 0.10| 0.14| 0.35| 311| |Taiwan_National Dong Hwa University | 0.35| 0.40| 0.19| 0.18| 0.00| 0.33| 0.49| 0.23| 0.39| 0.00| 0.30| 0.44| 0.39| 0.08| 0.30| 0.30| 0.27| 0.14| 0.75| 0.93| 0.40| 280| |New Zealand_University of Waikato | 0.34| 0.19| 0.38| 0.26| 0.33| 0.48| 0.64| 0.58| 0.46| 0.25| 0.89| 0.87| 0.83| 0.28| 0.73| 0.38| 0.37| 0.76| 0.37| 0.36| 0.56| 200| |USA_Washington State University | 0.34| 0.26| 0.76| 0.58| 0.67| 0.64| 0.28| 0.73| 0.62| 0.63| 0.72| 0.39| 0.41| 0.72| 0.56| 0.77| 0.72| 0.18| 0.86| 0.78| 0.62| 155| |Hong Kong_University of Hong Kong | 0.34| 0.28| 0.93| 0.78| 0.94| 0.95| 0.81| 0.77| 0.97| 0.93| 0.99| 0.98| 0.50| 0.92| 0.87| 0.95| 0.90| 0.21| 0.97| 0.83| 0.88| 19| |USA_Old Dominion University | 0.34| 0.23| 0.54| 0.41| 0.43| 0.42| 0.97| 0.65| 0.39| 0.35| 0.41| 0.17| 0.45| 0.53| 0.39| 0.69| 0.64| 0.57| 0.43| 0.20| 0.54| 212| |Russia_Pacific National University | 0.34| 0.23| 0.09| 0.07| 0.00| 0.04| 0.18| 0.03| 0.07| 0.00| 0.09| 0.30| 0.15| 0.08| 0.14| 0.09| 0.07| 0.06| 0.14| 0.25| 0.15| 381| |USA_Virginia Polytechnic Institute and State University | 0.34| 0.31| 0.76| 0.63| 0.87| 0.60| 0.62| 0.55| 0.66| 0.87| 0.76| 0.63| 0.37| 0.88| 0.67| 0.79| 0.73| 0.17| 0.89| 0.84| 0.73| 106| |Pakistan_NED University of Engineering and Technology | 0.34| 0.16| 0.04| 0.03| 0.00| 0.15| 0.08| 0.23| 0.12| 0.00| 0.04| 0.03| 0.97| 0.08| 0.27| 0.09| 0.07| 0.53| 0.10| 0.17| 0.16| 379| |USA_Portland State University | 0.33| 0.11| 0.26| 0.15| 0.36| 0.30| 0.00| 0.41| 0.32| 0.35| 0.68| 0.44| 0.24| 0.38| 0.43| 0.60| 0.55| 0.42| 0.45| 0.31| 0.40| 281| |Finland_Aalto University | 0.33| 0.72| 0.81| 0.86| 0.77| 0.86| 0.49| 0.73| 0.85| 0.79| 0.71| 0.85| 0.93| 0.80| 0.84| 0.64| 0.58| 0.75| 0.63| 0.73| 0.79| 57| |New Zealand_University of Auckland | 0.32| 0.15| 0.60| 0.39| 0.81| 0.71| 0.98| 0.73| 0.74| 0.80| 0.92| 0.91| 0.88| 0.84| 0.91| 0.51| 0.46| 0.66| 0.63| 0.65| 0.76| 78| |Hong Kong_Chinese University Hong Kong | 0.32| 0.21| 0.87| 0.67| 0.89| 0.95| 0.61| 0.82| 0.97| 0.89| 0.97| 0.91| 0.48| 0.82| 0.81| 0.95| 0.90| 0.35| 0.95| 0.64| 0.89| 18| |USA_Florida Atlantic University | 0.32| 0.14| 0.43| 0.28| 0.24| 0.27| 0.82| 0.38| 0.27| 0.15| 0.66| 0.52| 0.34| 0.30| 0.46| 0.52| 0.46| 0.45| 0.38| 0.25| 0.41| 272| |Portugal_University of Porto | 0.32| 0.63| 0.63| 0.68| 0.75| 0.68| 0.21| 0.52| 0.75| 0.67| 0.23| 0.64| 0.70| 0.68| 0.57| 0.31| 0.27| 0.91| 0.37| 0.57| 0.61| 163| |USA_Savannah College of Art and Design | 0.32| 0.29| 0.00| 0.00| 0.00| 0.02| 0.00| 0.01| 0.08| 0.00| 0.52| 0.85| 0.02| 0.08| 0.36| 0.68| 0.61| 0.02| 0.82| 0.70| 0.28| 340| |USA_Auburn University | 0.32| 0.36| 0.82| 0.70| 0.55| 0.41| 0.84| 0.41| 0.50| 0.47| 0.70| 0.44| 0.31| 0.64| 0.52| 0.83| 0.76| 0.51| 0.57| 0.24| 0.59| 176| |USA_Oakland University | 0.31| 0.19| 0.53| 0.37| 0.33| 0.33| 0.46| 0.40| 0.35| 0.25| 0.39| 0.20| 0.34| 0.35| 0.31| 0.55| 0.49| 0.95| 0.13| 0.04| 0.36| 301| |Switzerland_University of Lucerne | 0.31| 0.74| 0.53| 0.67| 0.29| 0.21| 0.78| 0.66| 0.22| 0.35| 0.87| 0.62| 0.76| 0.43| 0.68| 0.39| 0.36| 0.61| 0.23| 0.25| 0.59| 182| |Hungary_Eotvos Lorand University | 0.31| 0.47| 0.40| 0.41| 0.36| 0.44| 0.18| 0.73| 0.37| 0.35| 0.53| 0.49| 0.87| 0.28| 0.54| 0.34| 0.32| 0.30| 0.58| 0.71| 0.54| 213| |Russia_Novosibirsk State University of Economics and Management | 0.30| 0.14| 0.06| 0.05| 0.00| 0.02| 0.08| 0.06| 0.04| 0.00| 0.05| 0.17| 0.02| 0.08| 0.06| 0.00| 0.00| 0.99| 0.00| 0.08| 0.15| 380| |USA_California State University, Long Beach | 0.29| 0.07| 0.13| 0.08| 0.13| 0.18| 0.76| 0.32| 0.17| 0.10| 0.70| 0.35| 0.27| 0.21| 0.38| 0.49| 0.43| 0.28| 0.25| 0.13| 0.35| 312| |Spain_Complutense University of Madrid | 0.29| 0.36| 0.83| 0.71| 0.83| 0.48| 0.45| 0.40| 0.52| 0.78| 0.14| 0.58| 0.56| 0.76| 0.52| 0.28| 0.22| 0.96| 0.17| 0.14| 0.56| 203| |Russia_Reshetnev Siberian State University of Science and Technology | 0.29| 0.40| 0.10| 0.11| 0.36| 0.10| 0.28| 0.07| 0.10| 0.47| 0.10| 0.15| 0.19| 0.56| 0.24| 0.13| 0.08| 0.16| 0.14| 0.23| 0.26| 347| |Iran_University of Isfahan | 0.28| 0.58| 0.58| 0.62| 0.49| 0.41| 0.13| 0.16| 0.54| 0.10| 0.09| 0.09| 0.11| 0.08| 0.08| 0.35| 0.31| 0.98| 0.10| 0.05| 0.40| 282| |UK_Leeds Beckett University | 0.28| 0.14| 0.10| 0.08| 0.29| 0.18| 0.26| 0.43| 0.19| 0.40| 0.65| 0.53| 0.34| 0.43| 0.49| 0.34| 0.29| 0.93| 0.08| 0.03| 0.40| 285| |UK_University of Strathclyde | 0.28| 0.33| 0.75| 0.62| 0.61| 0.55| 0.64| 0.63| 0.57| 0.61| 0.84| 0.84| 0.76| 0.70| 0.80| 0.53| 0.44| 0.62| 0.55| 0.63| 0.69| 126| |Canada_Universite de Montreal | 0.27| 0.27| 0.95| 0.81| 0.80| 0.89| 0.57| 0.69| 0.91| 0.81| 0.86| 0.80| 0.70| 0.86| 0.82| 0.79| 0.69| 0.48| 0.84| 0.77| 0.81| 45| |USA_Kent State University | 0.27| 0.15| 0.61| 0.41| 0.46| 0.48| 0.98| 0.76| 0.38| 0.40| 0.59| 0.47| 0.39| 0.62| 0.52| 0.61| 0.52| 0.82| 0.27| 0.10| 0.59| 179| |Russia_Saint-Petersburg state University of Architecture and Construction | 0.27| 0.57| 0.06| 0.07| 0.09| 0.07| 0.06| 0.23| 0.06| 0.10| 0.08| 0.37| 0.10| 0.08| 0.14| 0.16| 0.11| 0.07| 0.11| 0.11| 0.17| 378| |China_Hunan University | 0.27| 0.51| 0.51| 0.51| 0.36| 0.59| 0.30| 0.85| 0.54| 0.40| 0.33| 0.14| 0.16| 0.38| 0.24| 0.45| 0.39| 0.39| 0.68| 0.75| 0.49| 234| |Italy_University of Florence | 0.27| 0.46| 0.95| 0.87| 0.51| 0.80| 0.72| 0.74| 0.71| 0.60| 0.34| 0.35| 0.57| 0.64| 0.48| 0.42| 0.37| 0.79| 0.50| 0.61| 0.65| 151| |UK_Glasgow Caledonian University | 0.26| 0.10| 0.39| 0.24| 0.19| 0.30| 0.86| 0.54| 0.28| 0.25| 0.63| 0.67| 0.53| 0.30| 0.53| 0.28| 0.21| 0.88| 0.16| 0.13| 0.42| 271| |Russia_Siberian State University of Water Transport | 0.26| 0.46| 0.08| 0.09| 0.00| 0.10| 0.08| 0.08| 0.10| 0.00| 0.12| 0.17| 0.19| 0.08| 0.13| 0.14| 0.10| 0.15| 0.16| 0.26| 0.14| 383| |Taiwan_Tatung University | 0.25| 0.27| 0.21| 0.16| 0.00| 0.31| 0.73| 0.14| 0.36| 0.00| 0.12| 0.15| 0.04| 0.08| 0.08| 0.26| 0.19| 0.74| 0.31| 0.35| 0.22| 363| |Japan_Kindai University | 0.25| 0.16| 0.09| 0.07| 0.13| 0.37| 0.77| 0.34| 0.31| 0.20| 0.46| 0.12| 0.07| 0.21| 0.20| 0.83| 0.72| 0.78| 0.25| 0.06| 0.32| 320| |Iraq_Middle Technical University | 0.25| 0.07| 0.02| 0.03| 0.13| 0.05| 0.03| 0.44| 0.03| 0.00| 0.03| 0.00| 0.99| 0.08| 0.27| 0.01| 0.01| 0.70| 0.03| 0.14| 0.20| 368| |Australia_James Cook University | 0.24| 0.20| 0.59| 0.43| 0.49| 0.89| 0.94| 0.87| 0.89| 0.44| 0.91| 0.54| 0.73| 0.66| 0.72| 0.65| 0.53| 0.92| 0.41| 0.29| 0.68| 132| |China_Xiangtan University | 0.24| 0.22| 0.16| 0.11| 0.09| 0.32| 0.31| 0.48| 0.29| 0.10| 0.33| 0.10| 0.08| 0.08| 0.13| 0.24| 0.16| 0.32| 0.48| 0.69| 0.30| 331| |Italy_University of Padua | 0.24| 0.27| 0.94| 0.79| 0.70| 0.85| 0.99| 0.81| 0.81| 0.66| 0.40| 0.23| 0.73| 0.62| 0.50| 0.39| 0.31| 0.96| 0.26| 0.27| 0.66| 146| |Netherlands_Wageningen University and Research Center | 0.24| 0.77| 0.87| 0.90| 0.90| 0.90| 0.44| 0.94| 0.84| 0.91| 0.67| 0.86| 0.93| 0.93| 0.87| 0.91| 0.81| 0.17| 0.95| 0.98| 0.86| 29| |Ireland_University of Limerick | 0.24| 0.34| 0.46| 0.39| 0.36| 0.50| 0.46| 0.48| 0.51| 0.40| 0.89| 0.71| 0.63| 0.38| 0.66| 0.35| 0.28| 0.56| 0.54| 0.71| 0.59| 181| |Iran_Shahid Beheshti University | 0.24| 0.69| 0.65| 0.73| 0.51| 0.10| 0.18| 0.26| 0.08| 0.40| 0.11| 0.11| 0.08| 0.24| 0.12| 0.46| 0.38| 0.03| 0.50| 0.42| 0.36| 306| |USA_University of Texas at Dallas | 0.23| 0.32| 0.49| 0.41| 0.63| 0.69| 0.96| 0.76| 0.62| 0.71| 0.50| 0.83| 0.61| 0.78| 0.69| 0.67| 0.55| 0.77| 0.46| 0.27| 0.68| 131| |Russia_Rostov State University of Economics | 0.23| 0.06| 0.11| 0.06| 0.00| 0.01| 0.08| 0.02| 0.02| 0.00| 0.07| 0.15| 0.00| 0.08| 0.06| 0.05| 0.03| 0.02| 0.06| 0.09| 0.07| 389| |Ireland_Dublin Institute of Technology | 0.22| 0.10| 0.11| 0.07| 0.13| 0.20| 0.14| 0.45| 0.18| 0.57| 0.64| 0.75| 0.80| 0.48| 0.68| 0.37| 0.29| 0.36| 0.24| 0.17| 0.38| 295| |Taiwan_National Changhua University of Education | 0.22| 0.37| 0.43| 0.38| 0.09| 0.30| 0.32| 0.15| 0.44| 0.00| 0.20| 0.41| 0.07| 0.08| 0.18| 0.32| 0.24| 0.62| 0.44| 0.49| 0.36| 307| |Ireland_University College Cork | 0.22| 0.22| 0.64| 0.47| 0.43| 0.65| 0.35| 0.77| 0.61| 0.25| 0.84| 0.72| 0.81| 0.24| 0.66| 0.57| 0.44| 0.46| 0.69| 0.81| 0.54| 208| |Ireland_Trinity College Dublin | 0.22| 0.24| 0.85| 0.65| 0.78| 0.85| 0.51| 0.81| 0.80| 0.77| 0.94| 0.90| 0.86| 0.81| 0.90| 0.67| 0.54| 0.56| 0.73| 0.80| 0.77| 68| |Iraq_Imam Jaafar Al-Sadiq University	0.22	0.58	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.10	0.18	0.03	0.00	0.18	0.08	0.07	0.04	0.00	0.08	0.14	0.08	386
Mexico_Autonomous University of Mexico State	0.21	0.61	0.11	0.13	0.24	0.12	0.67	0.11	0.12	0.25	0.18	0.05	0.35	0.35	0.22	0.27	0.18	0.18	0.17	0.19	0.24	358
Iran_K. N. Toosi University of Technology	0.21	0.52	0.81	0.77	0.33	0.66	0.05	0.23	0.94	0.25	0.36	0.09	0.08	0.30	0.19	0.46	0.36	0.87	0.60	0.55	0.45	254
Israel_Tel Aviv University	0.21	0.29	0.92	0.76	0.78	0.95	0.28	0.57	0.98	0.82	0.66	0.38	0.59	0.87	0.63	0.69	0.55	0.71	0.83	0.85	0.75	89
Italy_University of Pisa	0.21	0.48	0.77	0.72	0.51	0.84	0.96	0.82	0.81	0.60	0.34	0.31	0.64	0.62	0.48	0.37	0.27	0.95	0.30	0.28	0.61	166
UK_London Metropolitan University	0.20	0.08	0.28	0.15	0.33	0.20	0.97	0.21	0.22	0.40	0.77	0.96	0.64	0.43	0.71	0.40	0.30	0.97	0.05	0.02	0.44	257
Taiwan_Ming Chuan University	0.20	0.10	0.04	0.03	0.00	0.16	0.50	0.12	0.18	0.10	0.40	0.55	0.07	0.18	0.29	0.25	0.16	0.39	0.23	0.21	0.19	373
Thailand_Kasetsart University	0.20	0.18	0.25	0.17	0.46	0.19	0.93	0.19	0.18	0.51	0.35	0.06	0.69	0.48	0.39	0.46	0.34	0.10	0.53	0.46	0.40	283
North Macedonia_European University Skopje	0.20	0.44	0.06	0.06	0.00	0.00	0.00	0.02	0.03	0.00	0.48	0.92	0.00	0.08	0.37	0.16	0.09	0.27	0.03	0.01	0.17	376
Republic of Korea_Sogang University	0.20	0.21	0.57	0.42	0.53	0.50	0.23	0.20	0.70	0.57	0.41	0.54	0.18	0.32	0.36	0.72	0.57	0.30	0.81	0.74	0.49	235
Turkey_Istanbul Medipol University	0.20	0.98	0.03	0.05	0.00	0.16	0.03	0.10	0.19	0.00	0.20	0.13	0.05	0.08	0.10	0.51	0.39	0.47	0.24	0.11	0.27	346
Romania_University Politechica of Bucharest	0.19	0.01	0.28	0.07	0.60	0.38	0.09	0.23	0.43	0.51	0.09	0.18	0.39	0.24	0.21	0.23	0.14	0.53	0.51	0.73	0.33	315
USA_Northern Arizona University	0.19	0.13	0.32	0.19	0.40	0.31	0.30	0.83	0.23	0.35	0.27	0.26	0.38	0.48	0.34	0.51	0.39	0.47	0.30	0.16	0.35	309
Hong Kong_Hong Kong Polytechnic University	0.19	0.09	0.73	0.43	0.82	0.66	0.37	0.75	0.73	0.86	0.90	0.84	0.32	0.84	0.74	0.90	0.79	0.71	0.59	0.42	0.67	137
Taiwan_Feng Chia University	0.19	0.13	0.16	0.10	0.46	0.25	0.18	0.15	0.31	0.51	0.29	0.67	0.27	0.43	0.41	0.35	0.24	0.24	0.55	0.74	0.38	296
Ireland_University College Dublin	0.19	0.23	0.72	0.52	0.57	0.87	0.58	0.86	0.87	0.64	0.87	0.89	0.93	0.70	0.87	0.64	0.48	0.67	0.70	0.67	0.74	100
Turkey_Bogazici University	0.18	0.34	0.34	0.30	0.81	0.60	0.14	0.90	0.46	0.74	0.47	0.19	0.89	0.80	0.60	0.44	0.33	0.65	0.44	0.55	0.55	204
Republic of Korea_Kyungpook National University	0.18	0.10	0.68	0.41	0.43	0.74	0.33	0.30	0.89	0.40	0.43	0.34	0.29	0.38	0.35	0.78	0.61	0.47	0.84	0.70	0.56	196
Canada_University of Waterloo	0.17	0.20	0.58	0.41	0.86	0.77	0.67	0.63	0.85	0.84	0.90	0.75	0.69	0.89	0.82	0.69	0.52	0.70	0.68	0.56	0.77	77
Netherlands_University of Groningen	0.17	0.25	0.85	0.67	0.81	0.98	0.54	0.86	0.98	0.83	0.78	0.72	0.82	0.83	0.81	0.80	0.65	0.37	0.96	0.94	0.79	60
USA_Florida International University	0.17	0.04	0.78	0.37	0.29	0.51	0.55	0.68	0.45	0.25	0.47	0.41	0.50	0.53	0.48	0.77	0.60	0.58	0.50	0.24	0.54	214
Iraq_University of Samarra	0.16	0.00	0.05	0.00	0.00	0.02	0.04	0.09	0.02	0.00	0.00	0.00	0.00	0.08	0.00	0.03	0.03	0.46	0.02	0.04	0.05	390
Japan_Shibaura Institute of Technology	0.16	0.08	0.15	0.09	0.46	0.23	0.23	0.11	0.28	0.54	0.50	0.68	0.22	0.48	0.47	0.88	0.74	0.69	0.28	0.06	0.42	267
Portugal_ISCTE – University Institute of Lisbon	0.16	0.46	0.61	0.58	0.13	0.26	0.11	0.29	0.35	0.20	0.39	0.57	0.62	0.35	0.49	0.20	0.12	0.49	0.43	0.80	0.40	277
Chile_Pontificial Catholic University of Valparaiso	0.16	0.36	0.24	0.20	0.24	0.24	0.58	0.20	0.29	0.20	0.52	0.07	0.74	0.28	0.40	0.34	0.22	0.60	0.33	0.43	0.30	332
Russia_Belgorod State Technological University	0.15	0.00	0.00	0.00	0.19	0.03	0.00	0.02	0.04	0.15	0.30	0.50	0.02	0.08	0.21	0.20	0.12	0.02	0.33	0.81	0.18	375
USA_Texas A&M University	0.15	0.12	0.93	0.69	0.92	0.70	0.91	0.59	0.75	0.92	0.77	0.43	0.50	0.94	0.67	0.87	0.70	0.29	0.84	0.69	0.70	122
Japan_Tokyo University of Science	0.15	0.15	0.27	0.17	0.63	0.62	0.48	0.31	0.67	0.64	0.37	0.12	0.12	0.69	0.32	0.48	0.33	0.89	0.36	0.24	0.41	275
Australia_University of Tasmania	0.15	0.10	0.69	0.43	0.49	0.75	0.92	0.64	0.83	0.40	0.88	0.90	0.68	0.60	0.78	0.68	0.50	0.62	0.71	0.67	0.69	125
Italy_University of Ferrara	0.14	0.45	0.60	0.55	0.33	0.85	0.86	0.65	0.82	0.35	0.06	0.37	0.72	0.43	0.39	0.30	0.17	0.97	0.21	0.21	0.54	211
USA_University of Texas at Arlington	0.14	0.04	0.50	0.21	0.33	0.50	0.83	0.61	0.44	0.25	0.29	0.64	0.62	0.32	0.47	0.73	0.54	0.57	0.49	0.23	0.46	250
Jordan_Al-Ahliyya Amman University	0.14	0.19	0.00	0.00	0.09	0.10	0.00	0.09	0.10	0.00	0.80	0.99	0.61	0.18	0.65	0.22	0.13	0.00	0.00	0.00	0.26	349
Canada_University of Victoria	0.13	0.17	0.46	0.32	0.51	0.76	0.00	0.90	0.68	0.47	0.95	0.76	0.84	0.68	0.83	0.69	0.48	0.67	0.60	0.52	0.64	152
Jordan_University of Petra (UOP)	0.13	0.01	0.00	0.00	0.00	0.14	0.00	0.13	0.12	0.00	0.62	0.87	0.76	0.08	0.59	0.09	0.04	0.27	0.14	0.30	0.24	354
Australia_Charles Darwin University	0.13	0.28	0.42	0.34	0.29	0.65	0.54	0.53	0.70	0.20	0.77	0.93	0.54	0.32	0.65	0.82	0.63	0.68	0.60	0.37	0.59	178
Australia_University of Southern Queensland	0.13	0.18	0.41	0.29	0.09	0.36	0.35	0.53	0.37	0.35	0.77	0.66	0.74	0.35	0.64	0.53	0.34	0.88	0.22	0.10	0.46	251
Taiwan_National Chiayi University	0.13	0.12	0.12	0.08	0.00	0.23	0.24	0.10	0.28	0.00	0.11	0.21	0.06	0.08	0.10	0.34	0.20	0.25	0.53	0.67	0.24	355
Thailand_University of the Thai Chamber of Commerce	0.12	0.23	0.04	0.04	0.00	0.05	0.04	0.06	0.05	0.00	0.43	0.20	0.81	0.08	0.38	0.16	0.07	0.04	0.15	0.20	0.13	384
Canada_Simon Fraser University	0.12	0.09	0.50	0.29	0.58	0.76	0.78	0.67	0.80	0.57	0.91	0.89	0.78	0.64	0.82	0.71	0.47	0.66	0.68	0.48	0.69	123
Iraq_University of Kirkuk	0.11	0.06	0.06	0.04	0.00	0.06	0.26	0.08	0.04	0.00	0.40	0.03	0.97	0.08	0.37	0.13	0.05	0.05	0.11	0.32	0.13	385
Egypt_Alexandria University	0.11	0.32	0.35	0.30	0.40	0.14	0.21	0.20	0.14	0.20	0.15	0.17	0.90	0.35	0.39	0.14	0.06	0.05	0.50	0.96	0.31	326
Greece_University of Patras	0.11	0.35	0.40	0.36	0.24	0.34	0.22	0.35	0.32	0.20	0.09	0.25	0.58	0.08	0.24	0.15	0.06	0.82	0.23	0.78	0.28	345
Australia_Murdoch University	0.11	0.01	0.49	0.14	0.29	0.60	0.42	0.53	0.70	0.25	0.92	0.95	0.63	0.38	0.73	0.52	0.31	0.77	0.52	0.42	0.51	228
Ireland_Maynooth University	0.10	0.08	0.44	0.23	0.43	0.68	0.40	0.88	0.44	0.10	0.91	0.56	0.84	0.30	0.66	0.62	0.40	0.42	0.59	0.49	0.53	216
Belgium_Vrije Universiteit Brussels (VUB)	0.10	0.39	0.94	0.84	0.64	0.94	0.32	0.68	0.96	0.71	0.63	0.80	0.89	0.73	0.78	0.86	0.64	0.41	0.93	0.93	0.81	47
Australia_Deakin University	0.10	0.09	0.42	0.24	0.64	0.64	0.63	0.67	0.71	0.64	0.92	0.80	0.61	0.73	0.78	0.63	0.40	0.93	0.31	0.16	0.60	175
Germany_University of Gottingen	0.09	0.48	0.97	0.91	0.86	0.92	0.00	0.85	0.91	0.83	0.58	0.59	0.75	0.86	0.71	0.86	0.62	0.35	0.90	0.81	0.78	62
Canada_University of Guelph	0.09	0.08	0.53	0.30	0.75	0.70	0.90	0.48	0.84	0.74	0.70	0.44	0.61	0.00	0.43	0.83	0.58	0.63	0.72	0.51	0.60	170
Belgium_University of Antwerp	0.09	0.26	0.92	0.75	0.53	0.96	0.37	0.78	0.96	0.64	0.58	0.69	0.94	0.62	0.72	0.76	0.50	0.53	0.89	0.92	0.79	58
Iran_Babol Noshirvani University of Technology	0.09	0.23	0.30	0.22	0.29	0.88	0.07	0.98	0.89	0.15	0.00	0.02	0.09	0.26	0.07	0.28	0.13	0.94	0.36	0.42	0.41	273
Belgium_Universite Libre de Bruxelles	0.09	0.63	0.60	0.65	0.58	0.81	0.17	0.84	0.73	0.57	0.75	0.94	0.95	0.43	0.78	0.53	0.29	0.42	0.77	0.92	0.74	96
Latvia_Riga Technical University	0.08	0.30	0.54	0.45	0.29	0.20	0.20	0.44	0.20	0.25	0.65	0.53	0.78	0.48	0.62	0.35	0.17	0.09	0.58	0.86	0.47	243
Australia_University of Adelaide	0.08	0.06	0.91	0.53	0.73	0.97	0.90	0.95	0.96	0.76	0.95	0.89	0.72	0.83	0.86	0.84	0.58	0.63	0.84	0.83	0.82	40
Canada_Universite du Quebec a Montreal	0.08	0.12	0.43	0.27	0.63	0.44	0.46	0.51	0.46	0.64	0.53	0.69	0.58	0.78	0.66	0.43	0.21	0.80	0.34	0.29	0.52	226
Iran_Iran University of Science & Technology	0.06	0.06	0.88	0.50	0.57	0.75	0.41	0.29	0.97	0.47	0.00	0.05	0.07	0.24	0.07	0.70	0.41	0.59	0.87	0.80	0.49	233
Canada_Concordia University	0.06	0.10	0.44	0.26	0.43	0.42	0.23	0.39	0.53	0.44	0.84	0.88	0.53	0.60	0.72	0.50	0.24	0.80	0.37	0.28	0.52	222
Iraq_Madenat Al-elem University College	0.06	0.00	0.00	0.00	0.00	0.02	0.00	0.08	0.02	0.00	0.31	0.00	0.00	0.08	0.08	0.04	0.02	0.04	0.05	0.21	0.07	388
Taiwan_Chung Yuan Christian University	0.06	0.07	0.29	0.14	0.29	0.44	0.37	0.14	0.59	0.51	0.19	0.53	0.27	0.43	0.35	0.52	0.24	0.47	0.67	0.60	0.44	258
Australia_University of Wollongong	0.06	0.05	0.82	0.44	0.55	0.87	0.75	0.79	0.93	0.68	0.96	0.87	0.75	0.75	0.85	0.85	0.54	0.81	0.65	0.41	0.77	70
Australia_La Trobe University	0.06	0.02	0.71	0.28	0.36	0.74	0.88	0.63	0.86	0.44	0.92	0.89	0.46	0.56	0.72	0.80	0.47	0.75	0.66	0.41	0.67	136
Australia_Monash University	0.06	0.06	0.87	0.49	0.91	0.94	0.91	0.82	0.95	0.91	0.83	0.96	0.67	0.94	0.87	0.88	0.59	0.71	0.76	0.61	0.87	24
Iraq_Baghdad College Of Economic Sciences University	0.06	0.02	0.00	0.00	0.00	0.04	0.00	0.03	0.04	0.00	0.00	0.00	0.63	0.08	0.16	0.17	0.06	0.97	0.01	0.00	0.08	387
Thailand_Mahasarakham University	0.05	0.08	0.35	0.19	0.00	0.12	0.76	0.12	0.10	0.00	0.38	0.05	0.44	0.08	0.23	0.08	0.03	0.83	0.05	0.11	0.15	382
Germany_Ludwig Maximilian University of Munich	0.05	0.38	0.99	0.95	0.93	0.99	0.67	0.89	1.00	0.93	0.61	0.69	0.79	0.93	0.77	0.98	0.87	0.08	1.00	0.99	0.89	17
Canada_York University	0.05	0.03	0.44	0.18	0.67	0.57	0.38	0.60	0.61	0.74	0.78	0.82	0.59	0.82	0.77	0.73	0.39	0.65	0.55	0.27	0.58	186
Italy_Polytechnic University of Turin	0.04	0.20	0.63	0.45	0.72	0.62	0.75	0.44	0.77	0.69	0.17	0.60	0.60	0.64	0.51	0.44	0.17	0.75	0.58	0.59	0.55	205
Belgium_Katholieke Universiteit Leuven (KU Leuven)	0.04	0.14	0.95	0.74	0.92	0.95	0.32	0.77	0.95	0.92	0.66	0.65	0.94	0.92	0.81	0.87	0.53	0.49	0.89	0.90	0.77	69
Germany_University of Cologne	0.04	0.48	0.97	0.91	0.61	0.75	0.97	0.70	0.74	0.60	0.51	0.68	0.71	0.68	0.66	0.89	0.58	0.45	0.75	0.66	0.74	97
Germany_University of Wurzburg	0.04	0.42	0.97	0.89	0.49	0.99	0.42	0.84	0.98	0.51	0.65	0.51	0.79	0.62	0.65	0.84	0.49	0.20	0.99	0.98	0.81	46
Belgium_Ghent University	0.04	0.14	0.96	0.75	0.86	0.95	0.41	0.77	0.97	0.86	0.51	0.50	0.89	0.87	0.71	0.77	0.41	0.55	0.88	0.95	0.78	65
Egypt_Cairo University	0.03	0.06	0.46	0.22	0.73	0.24	0.32	0.38	0.22	0.66	0.21	0.14	0.64	0.74	0.43	0.19	0.06	0.95	0.08	0.07	0.36	302
Egypt_Kafrelsheikh University	0.03	0.14	0.22	0.13	0.00	0.15	0.07	0.62	0.13	0.00	0.22	0.09	0.97	0.08	0.33	0.10	0.03	0.52	0.11	0.27	0.29	338
Germany_Darmstadt University of Technology	0.03	0.13	0.98	0.85	0.64	0.81	0.84	0.43	0.91	0.57	0.54	0.70	0.71	0.66	0.66	0.92	0.60	0.21	0.96	0.84	0.73	102
France_Universite de Paris-Nord - Paris 13	0.03	0.18	0.43	0.30	0.19	0.52	0.13	0.44	0.62	0.00	0.72	0.45	0.51	0.24	0.48	0.17	0.04	0.75	0.49	0.86	0.47	247
Taiwan_Chaoyang University of Technology	0.03	0.02	0.11	0.05	0.46	0.18	0.40	0.09	0.22	0.51	0.23	0.39	0.05	0.43	0.27	0.44	0.15	0.28	0.36	0.24	0.30	335
Germany_University of Freiburg	0.02	0.05	1.00	0.89	0.79	0.98	0.12	0.74	0.98	0.74	0.69	0.81	0.77	0.79	0.78	0.91	0.57	0.24	0.98	0.99	0.75	86
Greece_Athens University of Economics and Business	0.02	0.08	0.45	0.25	0.19	0.29	0.51	0.28	0.38	0.20	0.12	0.26	0.82	0.21	0.35	0.20	0.05	0.31	0.60	0.89	0.38	294
Israel_Interdisciplinary Center Herzliya (IDC Herzliya)	0.02	0.02	0.00	0.00	0.00	0.20	0.00	0.34	0.21	0.00	0.09	0.83	0.60	0.08	0.40	0.65	0.21	0.85	0.13	0.13	0.29	337
Mexico_Universidad de Guadalajara	0.01	0.08	0.24	0.12	0.24	0.17	0.29	0.12	0.15	0.25	0.21	0.04	0.41	0.28	0.22	0.71	0.22	0.19	0.27	0.15	0.26	350
Germany_Humboldt University of Berlin	0.01	0.24	0.98	0.88	0.90	0.99	0.39	0.82	1.00	0.90	0.64	0.71	0.69	0.90	0.75	0.85	0.33	0.89	0.71	0.72	0.81	49
Germany_University of Konstanz	0.01	0.10	0.98	0.79	0.58	0.88	0.50	0.60	0.94	0.63	0.61	0.60	0.84	0.60	0.67	0.91	0.45	0.15	0.98	0.97	0.72	115
Germany_University of Erlangen Nuremberg	0.01	0.18	0.99	0.90	0.51	0.98	0.91	0.74	0.99	0.60	0.49	0.55	0.67	0.48	0.56	0.98	0.74	0.55	0.92	0.45	0.73	103
Germany_Free University of Berlin	0.01	0.16	0.99	0.91	0.87	1.00	0.57	0.72	1.00	0.88	0.61	0.79	0.65	0.88	0.75	0.89	0.37	0.87	0.82	0.68	0.82	43
Germany_Technical University of Berlin	0.01	0.07	0.99	0.87	0.88	0.88	0.82	0.58	0.95	0.87	0.55	0.82	0.68	0.88	0.75	0.96	0.58	0.31	0.94	0.74	0.81	51
Germany_RWTH Aachen University	0.01	0.17	0.99	0.93	0.86	0.98	0.90	0.79	0.98	0.86	0.51	0.78	0.65	0.86	0.72	0.95	0.53	0.24	0.98	0.85	0.83	35
Turkey_Istanbul University	0.00	0.07	0.80	0.47	0.72	0.32	0.35	0.19	0.39	0.70	0.41	0.32	0.14	0.70	0.39	0.46	0.09	0.11	0.83	0.96	0.42	270
Germany_University of Hannover	0.00	0.07	0.98	0.76	0.58	0.82	0.55	0.52	0.92	0.61	0.49	0.61	0.59	0.67	0.60	0.94	0.43	0.40	0.89	0.66	0.62	154
South Africa_University of South Africa	0.00	0.01	0.47	0.07	0.36	0.18	1.00	0.26	0.24	0.25	0.45	0.36	0.43	0.35	0.40	0.78	0.09	0.88	0.13	0.02	0.30	328

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a strong positive relationship between the two rankings.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.9348151

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 649416, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.9348151

Summary of Findings about League A

Only the first Median Top League A is significant (see Table 1), Q1, D1 Top Leagues cannot satisfy the all criteria, such as significance, stability, high correlation of partial ranks. However, the hierarchical biclustering found one bicluster what satisfies all of the three criteria.

Applying iBBiG on Reversed Normalized Data

To identify the lower league(s), the reverse data matrix is needed to be calculated firstly. Applying the iBBiG method on the reversed normalized data can specify the lower league biclusters.

rmtx <- 1-mtx 
rres <- iBBiG(binaryMatrix=binarize(rmtx,threshold = NA),nModules = 2,alpha=0.33
              ,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## [1] "Threshold:  0.5"
## Module:  1 ... done
## Module:  2 ... done

summary(rres) 

## 
## An object of class iBBiG 
## 
## Number of Clusters found:  2 
## 
## First  2  Cluster scores and sizes:
##                         M 1 M 2
## Cluster Score      3904.349 686
## Number of Rows:     430.000 343
## Number of Columns:   17.000   2

The results above show that the iBBiG algorithm found 2 biclusters on the reversed data. In the first bicluster there are 430 rows (HEIs) and 17 columns (indicators), while the second bicluster has 343 rows (HEIs) and 2 columns (indicators). The next step is to calculate F-tests to determine which bicluster is significant.

Obs.FStat <- NULL 
for (i in c(1:rres@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=rmtx,bicResult=rres,number=i) 
  } 
kable(Obs.FStat,caption = "**Table 9** The results of row and column effects of the reversed data for the two biclusters")

Table 9 The results of row and column effects of the reversed data for the two biclusters

Fstat PValue Row Effect 6.995732 0 Column Effect 16.394468 0 Tukey test 29.941998 0

Fstat PValue Row Effect 3.2060341 0.0000000 Column Effect 0.2153001 0.6429398 Tukey test 0.0113277 0.9153023

In Table 9 the results of the F-tests can be seen. In the case of the first bicluster, both the row and column effect are significant. On the other hand, in the case of the second bicluster the row effect is not significant; thus the second bicluster is not significant. Only the first bicluster is significant which is the lower league (League C).

Calculating Lower League C Bicluster

The next step is to identify the lower league bicluster.

## [1] "Threshold:  0.5"
## Module:  1 ... done

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 3904.349 and 
##   430 Rows and  17 columns

The results of the iBBiG algorithm on the reversed data can be seen above. The algorithm found one bicluster in which there are 430 rows (HEIs) and 17 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant or not.

Calculating F-tests of the Lower League C Bicluster

In Table 5 the results of the row and column effects (F-tests) can be read. Both the row and column effects are significant, so the lower league bicluster is significant.

Obs.FStat <- NULL 
for (i in c(1:rres@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=rmtx,bicResult=rres,number=i) 
  } 
kable(Obs.FStat,caption = "**Table 10** The results of row and column effects of the lower league")

Table 10 The results of row and column effects of the lower league

Fstat PValue Row Effect 6.995732 0 Column Effect 16.394468 0 Tukey test 29.941998 0

To see the differences between those HEIs that are included in the lower league and those that are not in the lower league, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 19). On Fig. 19 the red line indicates those HEIs that are included in the lower league, while the black line shows the remaining HEIs. The HEIs in the lower league have lower means, medians, and variances.

exploreBic(dset=mtx,bres=rres,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 19 Mean, median, variance and MAD for lower leauge HEIs

One can do the same for the columns (indicators). Fig. 20 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. The red line indicates those indicators that are in the lower league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=rres,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 20 Mean, median, variance and MAD for lower leauge indicators

Heat Maps of the Lower League C

Fig. 21 depicts the heat map of the lower league. The lower league contains 430 HEIs and 17 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=rres,number=1,paleta=bluered(100),beamercolor = TRUE)

Fig. 21 Heat map of the lower leauge

Fig. 22 shows results of iBBiG on reversed normalized data. The lower league can be seen in the upper left corner of Fig. 22 which is enlarged on Fig. 21.

drawHeatmap(x=mtx,bicResult=rres,local=FALSE,number=1,paleta=bluered(100),beamercolor = TRUE) 

Fig. 22 Heat map of the output after applying iBBiG on reversed normalized data

Checking the stability of the Lower League C Bicluster

The next step is to check the stability of the lower league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=rres,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 0.9340393 1.1587810
##   [2,] 1.0864135 0.8941779
##   [3,] 1.0682840 1.2686315
##   [4,] 1.0986725 0.5775974
##   [5,] 0.9164469 1.2806748
##   [6,] 0.9362912 0.5506147
##   [7,] 1.0006288 1.0249467
##   [8,] 0.9006263 1.8089787
##   [9,] 0.9936582 0.6912787
##  [10,] 0.9864846 1.0536790
##  [11,] 0.9808971 0.5698071
##  [12,] 1.0629447 0.9948455
##  [13,] 0.9280725 1.3551924
##  [14,] 0.9793019 1.5244218
##  [15,] 1.0611563 0.8705833
##  [16,] 1.1414080 0.7284920
##  [17,] 1.0019560 0.8576313
##  [18,] 1.0986342 0.7378892
##  [19,] 0.9672636 1.1793005
##  [20,] 0.9187165 0.8816088
##  [21,] 1.0582440 1.3161186
##  [22,] 1.0680947 0.7518328
##  [23,] 0.9961640 1.1125051
##  [24,] 1.0601279 0.6580757
##  [25,] 0.9941924 1.2917385
##  [26,] 0.9683676 0.4780805
##  [27,] 0.9396512 1.0734670
##  [28,] 1.0555915 0.9061563
##  [29,] 1.0485873 0.8852000
##  [30,] 0.8828026 1.2710385
##  [31,] 0.9203372 0.8734621
##  [32,] 0.9537798 0.7498350
##  [33,] 0.7923910 1.1531130
##  [34,] 0.9775853 1.0582386
##  [35,] 0.9422213 1.4764410
##  [36,] 0.9206174 1.1959911
##  [37,] 0.9747330 0.4724154
##  [38,] 1.0293999 0.7909041
##  [39,] 0.9856884 1.6238014
##  [40,] 1.0639676 1.1564874
##  [41,] 1.1338556 0.7535590
##  [42,] 0.9630277 1.1183591
##  [43,] 1.0825844 0.8191844
##  [44,] 0.8737495 0.7097833
##  [45,] 1.0370645 1.0867830
##  [46,] 1.0203154 1.2475277
##  [47,] 1.0008880 0.7393900
##  [48,] 1.0356046 0.6218392
##  [49,] 1.0323543 1.6271046
##  [50,] 0.9596680 1.0227117
##  [51,] 0.9221662 0.8044236
##  [52,] 0.9661657 0.5776789
##  [53,] 0.9192206 1.3631454
##  [54,] 1.0384024 0.9944950
##  [55,] 0.9647707 0.7773826
##  [56,] 0.8859252 0.9876341
##  [57,] 1.1144698 1.5852183
##  [58,] 0.9138342 0.7125369
##  [59,] 1.0159799 1.3149507
##  [60,] 0.9943170 0.8231700
##  [61,] 0.9428632 0.5469518
##  [62,] 1.0270023 1.1288021
##  [63,] 0.9454882 1.1487804
##  [64,] 0.9988466 1.2251444
##  [65,] 1.0014411 0.8946767
##  [66,] 0.9922708 1.2642927
##  [67,] 1.0421091 0.8349491
##  [68,] 0.9989845 0.8120099
##  [69,] 1.0964267 0.9551519
##  [70,] 0.9416845 1.5130061
##  [71,] 1.0556345 0.7547419
##  [72,] 1.1628451 1.1479847
##  [73,] 0.8983307 0.6624390
##  [74,] 1.0167932 0.6354636
##  [75,] 0.9943982 1.4847467
##  [76,] 1.0495664 0.9172838
##  [77,] 1.0591524 0.9459405
##  [78,] 0.9265992 1.4322529
##  [79,] 0.9274006 1.2542660
##  [80,] 0.9558407 0.7740541
##  [81,] 0.9878011 0.6426957
##  [82,] 0.9184537 0.8035013
##  [83,] 0.9730141 0.9287308
##  [84,] 0.8694303 0.7545352
##  [85,] 0.9611491 0.7633971
##  [86,] 0.8987721 0.8955948
##  [87,] 1.0081818 1.2751852
##  [88,] 1.0520708 1.7988252
##  [89,] 0.9711074 0.7373232
##  [90,] 1.0620300 1.0778651
##  [91,] 1.1092772 1.0076845
##  [92,] 0.9065286 1.2021386
##  [93,] 1.0363814 1.3765398
##  [94,] 1.0008030 0.8345422
##  [95,] 1.0198712 1.0625564
##  [96,] 1.1098589 0.4265016
##  [97,] 1.0789944 0.7459493
##  [98,] 1.0474617 1.9277439
##  [99,] 1.0214080 0.9586083
## [100,] 1.1351635 0.8724236
## 
## $observedFstatRow
## [1] 6.995732
## 
## $observedFstatCol
## [1] 16.39447
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

Since the bootstrapPvalueCol are and bootstrapPvalueCol lower than 0.01, the bicluster is stable.

Calculating Partial Rankings for Lower League C

The next step is to calculate partial rankings based on the indicators and HEIs in the lower league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR’s indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 13 shows the result of partial ranking in the case of the lower league.

C<-biclust::bicluster(mtx,rres,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 13** League C by iBBiG",digits = 2)

Table 13 League C by iBBiG

	T3	T4	T5	R1	R2	R3	R4	R5	I1	I2	I3	I4	I5	F1	F2	F4	F5	Overall_Score	Rank
Belarus_National Institute of Higher Education	0.12	0.00	0.19	0.00	0.05	0.00	0.00	0.15	0.00	0.00	0.00	0.26	0.05	0.94	1.00	0.98	0.75	0.52	250
Iraq_Al-Karkh University of Science	0.00	0.00	0.00	0.03	0.00	0.03	0.03	0.00	0.24	0.00	1.00	0.08	0.32	0.01	0.01	0.20	1.00	0.30	362
Iraq_University of Information Technology and Communications	0.00	0.00	0.00	0.01	0.00	0.02	0.02	0.00	0.00	0.00	1.00	0.08	0.26	0.11	0.86	0.13	0.21	0.37	323
Iraq_Al-Qasim green university Iraq	0.00	0.00	0.00	0.06	0.00	0.14	0.07	0.00	0.00	0.00	0.99	0.08	0.26	0.09	0.63	0.09	0.12	0.35	337
Russia_European University at St. Petersburg	0.00	0.00	0.33	0.10	0.00	0.17	0.17	0.31	0.55	0.77	0.11	0.08	0.37	0.25	0.88	0.24	0.36	0.43	286
Russia_Mechnikov St Petersburg State Medical Academy	0.03	0.03	0.00	0.11	0.73	0.49	0.06	0.00	0.03	0.40	0.67	0.08	0.29	0.62	0.96	0.06	0.01	0.51	255
Brazil_A.C.Camargo Cancer Center	0.90	1.00	0.00	0.66	0.99	0.32	0.86	0.00	0.00	0.05	0.41	0.08	0.12	1.00	1.00	0.36	0.01	0.83	52
Kazakhstan_Shakarim University	0.04	0.04	0.00	0.02	0.97	0.02	0.02	0.00	0.00	0.00	0.96	0.08	0.25	0.02	0.10	0.03	0.39	0.31	353
Japan_Yokohama City University	0.23	0.60	0.19	0.49	0.68	0.48	0.44	0.15	0.28	0.13	0.09	0.43	0.22	0.19	0.70	0.30	0.43	0.54	242
Russia_Bauman Moscow State Technical University	0.28	0.78	0.79	0.08	0.10	0.05	0.09	0.76	0.46	0.41	0.05	0.68	0.40	0.17	0.64	0.62	0.94	0.69	153
Iraq_Hawler Medical University	0.03	0.05	0.00	0.00	0.06	0.00	0.00	0.00	0.19	0.11	0.00	0.08	0.08	0.44	0.87	0.29	0.18	0.24	387
Russia_Ufa State Aviation Technical University	0.04	0.06	0.24	0.09	0.04	0.24	0.08	0.31	0.03	0.09	0.51	0.43	0.26	0.03	0.10	0.01	0.01	0.23	391
Kazakhstan_Al-Farabi Kazakh National University	0.23	0.39	0.33	0.07	0.39	0.07	0.08	0.15	0.71	0.55	0.90	0.60	0.70	0.06	0.26	0.32	0.88	0.79	71
Kazakhstan_L.N. Gumilyov Eurasian National University	0.08	0.15	0.43	0.11	0.23	0.20	0.08	0.25	0.60	0.17	0.94	0.24	0.49	0.04	0.13	0.07	0.39	0.49	261
China_Southern Medical University - China	0.44	0.77	0.24	0.39	0.87	0.37	0.37	0.00	0.11	0.31	0.08	0.08	0.13	0.30	0.72	0.56	0.70	0.68	157
Japan_University of Yamanashi	0.26	0.50	0.19	0.39	0.89	0.25	0.38	0.47	0.20	0.21	0.14	0.18	0.17	0.53	0.86	0.33	0.18	0.70	144
Russia_Lobachevsky University	0.38	0.65	0.57	0.16	0.68	0.13	0.18	0.57	0.24	0.42	0.33	0.60	0.40	0.11	0.30	0.32	0.83	0.74	113
Japan_Gifu University	0.31	0.56	0.29	0.36	0.88	0.16	0.44	0.20	0.55	0.24	0.16	0.48	0.35	0.21	0.54	0.28	0.36	0.76	94
Russia_Saint Petersburg State University	0.38	0.72	0.88	0.30	0.20	0.23	0.37	0.83	0.34	0.58	0.52	0.78	0.56	0.20	0.50	0.46	0.77	0.92	15
Japan_Tottori University	0.23	0.38	0.09	0.33	0.79	0.16	0.40	0.10	0.31	0.11	0.15	0.21	0.18	0.25	0.58	0.18	0.15	0.55	229
Canada_University of Quebec at Chicoutimi	0.00	0.00	0.19	0.24	0.00	0.37	0.22	0.25	0.00	0.84	0.60	0.38	0.46	0.43	0.78	0.67	0.66	0.60	198
Japan_Kumamoto University	0.31	0.53	0.33	0.41	0.70	0.25	0.44	0.47	0.25	0.36	0.22	0.56	0.34	0.59	0.85	0.47	0.32	0.82	54
Spain_IQS Universitat Ramon Llull	0.05	0.19	0.00	0.42	0.08	0.68	0.37	0.10	0.47	0.65	0.86	0.08	0.52	0.44	0.78	0.34	0.48	0.73	123
Japan_Okayama University	0.33	0.54	0.46	0.53	0.44	0.34	0.54	0.51	0.32	0.41	0.29	0.64	0.41	0.48	0.79	0.43	0.34	0.77	86
Russia_Tver State Technical University	0.19	0.28	0.09	0.10	0.14	0.06	0.10	0.00	0.00	0.67	0.48	0.08	0.30	0.06	0.15	0.11	0.27	0.38	314
Russia_Bashkirian State Medical University	0.06	0.98	0.00	0.07	0.08	0.10	0.07	0.00	0.07	0.44	0.18	0.08	0.18	0.13	0.31	0.06	0.05	0.27	379
Russia_Kursk State Medical University	0.35	0.79	0.00	0.06	0.55	0.11	0.05	0.00	0.04	0.96	0.19	0.08	0.31	0.06	0.14	0.06	0.09	0.37	319
Russia_Sechenov University	0.28	0.55	0.36	0.12	0.21	0.09	0.14	0.40	0.45	0.68	0.32	0.60	0.51	0.41	0.74	0.18	0.08	0.58	216
Belarus_Belarusian State University	0.08	0.09	0.40	0.23	0.08	0.89	0.14	0.31	0.49	0.46	0.98	0.43	0.60	0.09	0.19	0.27	0.78	0.79	70
Ukraine_National University of Ostroh Academy	0.20	0.37	0.13	0.01	0.14	0.09	0.02	0.51	0.57	0.06	0.00	0.43	0.26	0.03	0.05	0.02	0.03	0.32	351
Ukraine_National Technical University Kharkiv Polytechnic Institute	0.12	0.20	0.19	0.08	0.34	0.08	0.08	0.35	0.08	0.47	0.63	0.21	0.34	0.02	0.05	0.04	0.21	0.35	332
Russia_Siberian State Medical University	0.08	0.14	0.00	0.12	0.22	0.15	0.12	0.00	0.10	0.76	0.14	0.08	0.26	0.14	0.31	0.10	0.11	0.26	384
China_Guangzhou Medical University	0.12	0.35	0.00	0.40	0.55	0.43	0.37	0.00	0.52	0.10	0.12	0.08	0.19	0.14	0.30	0.27	0.61	0.54	235
India_Manipal Academy of Higher Education	0.23	0.42	0.43	0.17	0.92	0.17	0.18	0.44	0.40	0.54	0.24	0.60	0.44	0.21	0.45	0.25	0.34	0.74	109
Japan_Yamagata University	0.19	0.31	0.00	0.36	0.94	0.23	0.38	0.10	0.32	0.11	0.21	0.21	0.20	0.47	0.76	0.40	0.31	0.65	169
Russia_Gubkin Russian State University of Oil and Gas	0.07	0.15	0.13	0.11	0.07	0.05	0.13	0.54	0.06	0.36	0.26	0.53	0.30	0.24	0.51	0.41	0.59	0.48	269
USA_The New School	0.18	0.32	0.49	0.16	0.86	0.57	0.15	0.44	0.36	0.93	0.19	0.66	0.54	0.51	0.78	0.20	0.07	0.78	81
Japan_Toyohashi University of Technology	0.31	0.40	0.43	0.37	0.92	0.14	0.51	0.54	0.33	0.38	0.11	0.43	0.30	0.36	0.67	0.47	0.51	0.78	80
Ukraine_National Taras Shevchenko University of Kyiv	0.26	0.45	0.63	0.18	0.78	0.12	0.17	0.57	0.10	0.17	0.77	0.43	0.36	0.05	0.12	0.07	0.19	0.60	196
Japan_Osaka City University	0.38	0.57	0.24	0.41	0.72	0.22	0.47	0.25	0.43	0.21	0.20	0.38	0.30	0.67	0.85	0.38	0.18	0.73	120
Argentina_Austral University (Argentina)	0.05	0.14	0.19	0.14	0.73	0.31	0.11	0.35	0.32	0.38	0.57	0.48	0.44	0.14	0.29	0.05	0.04	0.43	287
Russia_Perm National Research Polytechnic University	0.13	0.20	0.09	0.09	0.13	0.03	0.13	0.10	0.06	0.39	0.04	0.08	0.13	0.15	0.30	0.59	0.94	0.40	305
China_Jiangnan University	0.22	0.27	0.29	0.43	0.34	0.40	0.47	0.31	0.17	0.09	0.13	0.21	0.13	0.31	0.59	0.55	0.64	0.56	228
Russia_Kazan National Research Technical University named after A.N. Tupolev	0.17	0.27	0.19	0.09	0.15	0.06	0.12	0.10	0.27	0.48	0.15	0.18	0.26	0.20	0.42	0.47	0.74	0.46	274
Bulgaria_University of Sofia	0.27	0.35	0.43	0.23	0.39	0.59	0.18	0.51	0.19	0.32	0.90	0.32	0.43	0.05	0.10	0.13	0.50	0.59	211
USA_University of Vermont	0.45	0.58	0.29	0.57	0.80	0.72	0.50	0.20	0.23	0.35	0.34	0.26	0.29	0.63	0.82	0.43	0.26	0.72	126
Taiwan_National Central University	0.31	0.56	0.36	0.40	0.31	0.35	0.39	0.31	0.56	0.50	0.48	0.38	0.48	0.29	0.54	0.73	1.00	0.92	14
China_Jiangsu University	0.10	0.20	0.00	0.28	0.45	0.51	0.24	0.00	0.78	0.23	0.04	0.08	0.27	0.15	0.26	0.34	0.86	0.51	254
India_Jamia Millia Islamia	0.67	0.79	0.13	0.17	0.35	0.31	0.14	0.10	0.25	0.15	0.42	0.18	0.24	0.20	0.40	0.09	0.23	0.51	257
Pakistan_Institute of Space Technology	0.00	0.00	0.00	0.03	0.00	0.00	0.01	0.00	0.00	0.00	1.00	0.08	0.26	0.18	0.35	0.13	0.17	0.20	399
Tunisia_University of Monastir	0.35	0.52	0.29	0.20	0.10	0.14	0.23	0.10	0.05	0.11	0.86	0.43	0.36	0.01	0.01	0.02	0.11	0.34	339
Japan_Chiba University	0.48	0.63	0.33	0.52	0.53	0.30	0.57	0.31	0.33	0.27	0.23	0.35	0.29	0.30	0.53	0.47	0.61	0.77	90
Republic of Korea_Hallym University	0.13	0.16	0.00	0.44	0.36	0.15	0.60	0.00	0.26	0.27	0.05	0.08	0.15	0.34	0.60	0.37	0.41	0.40	309
Japan_University of the Ryukyus	0.14	0.21	0.58	0.36	0.34	0.18	0.38	0.44	0.27	0.13	0.28	0.60	0.31	0.51	0.74	0.27	0.12	0.65	171
Slovakia_Comenius University in Bratislava	0.38	0.68	0.43	0.35	0.64	0.45	0.31	0.20	0.26	0.61	0.87	0.38	0.54	0.13	0.24	0.37	0.81	0.74	114
Spain_Polytechnic University of Valencia	0.24	0.38	0.65	0.35	0.10	0.39	0.36	0.66	0.15	0.53	0.52	0.70	0.48	0.27	0.48	0.36	0.62	0.69	151
Japan_Kanazawa University	0.41	0.56	0.29	0.47	0.74	0.24	0.52	0.15	0.25	0.30	0.16	0.43	0.28	0.61	0.81	0.55	0.44	0.77	92
Russia_Magnitogorsk State Technical University	0.04	0.05	0.00	0.05	0.04	0.03	0.06	0.00	0.00	0.19	0.07	0.08	0.07	0.06	0.12	0.16	0.47	0.18	402
Russia_RANEPA, The Russian Presidential Academy of National Economy and Public Administration	0.18	0.31	0.13	0.04	0.18	0.15	0.07	0.15	0.38	0.25	0.16	0.43	0.30	0.44	0.68	0.38	0.40	0.42	300
Japan_Osaka Prefecture University	0.37	0.50	0.24	0.44	0.86	0.20	0.48	0.51	0.36	0.20	0.09	0.48	0.28	0.29	0.51	0.35	0.42	0.59	206
Iraq_University of AL-Qadisiyah	0.14	0.15	0.00	0.08	0.11	0.51	0.05	0.15	0.16	0.03	0.98	0.08	0.31	0.01	0.01	0.03	0.46	0.33	346
Tunisia_Universite de Tunis El Manar	0.62	0.84	0.19	0.22	0.08	0.16	0.24	0.20	0.32	0.10	0.77	0.53	0.43	0.02	0.04	0.19	0.88	0.53	244
Thailand_Mahidol University	0.25	0.40	0.68	0.37	0.33	0.34	0.36	0.66	0.53	0.21	0.71	0.35	0.45	0.95	0.96	0.63	0.12	0.78	79
Russia_The New Economic School	0.00	0.00	0.13	0.22	0.00	0.20	0.29	0.10	0.89	0.10	0.97	0.08	0.51	0.73	0.85	0.34	0.16	0.54	239
Ukraine_Kharkiv National University of Radio Electronics	0.14	0.17	0.13	0.07	0.13	0.21	0.05	0.31	0.04	0.47	0.59	0.08	0.29	0.03	0.05	0.04	0.10	0.31	355
Spain_University of Valladolid	0.17	0.99	0.09	0.26	0.12	0.25	0.24	0.15	0.29	0.28	0.47	0.48	0.38	0.15	0.24	0.12	0.19	0.56	226
Russia_Altai State University	0.12	0.29	0.09	0.12	0.60	0.18	0.12	0.10	0.36	0.61	0.57	0.08	0.40	0.08	0.14	0.19	0.47	0.48	267
Russia_Far Eastern Federal University	0.16	0.25	0.13	0.17	0.11	0.11	0.20	0.31	0.62	0.74	0.33	0.21	0.47	0.37	0.60	0.30	0.24	0.55	231
Ukraine_Poltava National Technical Yuri Kondratyuk University	0.00	0.00	0.09	0.03	0.00	0.04	0.04	0.10	0.00	0.30	0.02	0.08	0.09	0.00	0.00	0.00	0.00	0.06	425
Ukraine_Sumy State University	0.26	0.26	0.46	0.13	0.69	0.13	0.11	0.51	0.04	0.60	0.89	0.43	0.49	0.04	0.06	0.11	0.43	0.64	173
Spain_University of Zaragoza	0.67	0.80	0.36	0.42	0.83	0.43	0.36	0.40	0.13	0.33	0.57	0.43	0.36	0.15	0.25	0.22	0.41	0.86	31
Iraq_University of Baghdad	0.29	0.44	0.33	0.07	0.65	0.20	0.05	0.31	0.17	0.03	0.83	0.18	0.30	0.13	0.19	0.05	0.08	0.52	249
Romania_Grigore T. Popa University of Medicine and Pharmacy	0.14	0.21	0.13	0.31	0.23	0.20	0.38	0.00	0.03	0.85	0.24	0.08	0.29	0.11	0.18	0.04	0.04	0.35	335
Russia_Perm State University	0.07	0.09	0.19	0.12	0.16	0.04	0.15	0.15	0.12	0.10	0.06	0.08	0.07	0.08	0.14	0.16	0.40	0.25	386
Japan_Keio University	0.25	0.34	0.83	0.42	0.47	0.40	0.35	0.82	0.54	0.37	0.16	0.68	0.44	0.54	0.73	0.47	0.37	0.77	85
Iraq_Mustansiriyah University	0.16	0.22	0.13	0.05	0.70	0.17	0.03	0.15	0.05	0.02	0.91	0.08	0.26	0.12	0.18	0.01	0.01	0.33	347
Russia_Kazan National Research Technological University	0.15	0.29	0.09	0.11	0.38	0.05	0.13	0.00	0.08	0.51	0.04	0.08	0.17	0.12	0.18	0.31	0.66	0.38	315
Russia_Kazan Federal University	0.36	0.43	0.65	0.22	0.76	0.27	0.21	0.57	0.50	0.60	0.58	0.28	0.49	0.19	0.33	0.31	0.57	0.73	124
Spain_Polytechnic University of Catalonia	0.40	0.54	0.68	0.33	0.37	0.34	0.36	0.69	0.31	0.66	0.67	0.68	0.59	0.22	0.38	0.32	0.54	0.82	55
China_Jilin University	0.49	0.68	0.24	0.43	0.43	0.39	0.41	0.20	0.30	0.18	0.09	0.32	0.21	0.31	0.51	0.51	0.65	0.64	172
Lithuania_Vilnius University	0.25	0.39	0.40	0.35	0.50	0.48	0.30	0.31	0.61	0.45	0.71	0.43	0.55	0.13	0.20	0.43	0.91	0.86	33
Russia_Russian New University	0.12	0.24	0.09	0.03	0.15	0.04	0.03	0.10	0.16	0.48	0.00	0.08	0.17	0.06	0.10	0.09	0.22	0.27	378
Russia_Moscow Pedagogical State University	0.12	0.18	0.24	0.09	0.26	0.07	0.09	0.10	0.11	0.49	0.28	0.21	0.26	0.10	0.16	0.08	0.11	0.31	354
Russia_Ural Federal University	0.17	0.16	0.58	0.21	0.13	0.09	0.25	0.40	0.72	0.47	0.30	0.43	0.48	0.17	0.30	0.42	0.78	0.61	193
Tunisia_Universite de Carthage	0.33	0.57	0.00	0.16	0.83	0.17	0.17	0.10	0.13	0.05	0.93	0.08	0.29	0.01	0.01	0.02	0.09	0.42	299
Spain_Charles III University of Madrid	0.31	0.47	0.64	0.24	0.29	0.31	0.27	0.57	0.47	0.64	0.73	0.43	0.57	0.17	0.28	0.23	0.47	0.69	146
Russia_Voronezh State University	0.21	0.27	0.19	0.13	0.19	0.07	0.16	0.31	0.23	0.48	0.19	0.43	0.33	0.07	0.12	0.12	0.31	0.41	302
China_Shantou University	0.09	0.13	0.09	0.40	0.21	0.44	0.34	0.00	0.67	0.06	0.26	0.18	0.28	0.48	0.68	0.46	0.41	0.47	272
Republic of Korea_Kookmin University	0.18	0.22	0.09	0.22	0.21	0.26	0.18	0.15	0.38	0.47	0.13	0.21	0.29	0.17	0.28	0.32	0.59	0.39	310
USA_Creighton University	0.99	0.98	0.24	0.45	0.68	0.70	0.33	0.35	0.20	0.42	0.35	0.53	0.37	0.70	0.82	0.21	0.06	0.96	5
Russia_Russian State University for the Humanities	0.11	0.08	0.49	0.05	0.05	0.06	0.09	0.47	0.24	0.31	0.03	0.48	0.26	0.00	0.00	0.01	0.10	0.23	392
Ukraine_Kyiv National Economic University	0.11	0.15	0.36	0.00	0.20	0.00	0.01	0.54	0.04	0.05	1.00	0.43	0.38	0.02	0.03	0.01	0.02	0.37	321
Russia_Saratov State University	0.20	0.33	0.24	0.21	0.22	0.15	0.22	0.25	0.08	0.31	0.44	0.18	0.24	0.16	0.23	0.44	0.82	0.54	241
USA_West Virginia University	0.59	0.70	0.19	0.39	0.66	0.59	0.34	0.25	0.66	0.45	0.27	0.28	0.41	0.23	0.38	0.35	0.48	0.66	166
Russia_Northeast Federal University	0.69	0.81	0.09	0.13	0.66	0.28	0.11	0.00	0.55	0.22	0.66	0.08	0.38	0.20	0.32	0.20	0.22	0.45	280
Russia_Moscow Aviation Institute	0.37	0.61	0.55	0.07	0.87	0.04	0.10	0.51	0.30	0.43	0.03	0.48	0.31	0.23	0.37	0.44	0.76	0.64	174
Colombia_Universidad Pontificia Bolivariana de Medellin-Colombia	0.05	0.12	0.24	0.13	0.15	0.30	0.10	0.60	0.16	0.09	0.84	0.60	0.42	0.25	0.41	0.20	0.18	0.42	291
Russia_National Research University of Electronic Technology (MIET)	0.19	0.24	0.29	0.12	0.12	0.04	0.17	0.31	0.23	0.24	0.21	0.56	0.31	0.41	0.60	0.79	0.91	0.64	177
Russia_Novosibirsk State Technical University	0.10	0.14	0.43	0.15	0.07	0.10	0.16	0.47	0.17	0.75	0.29	0.43	0.41	0.10	0.14	0.21	0.49	0.54	243
Poland_Jagiellonian University	0.27	0.58	0.68	0.41	0.25	0.47	0.40	0.63	0.21	0.43	0.53	0.53	0.42	0.18	0.29	0.35	0.60	0.76	97
Russia_Ryazan State Medical University	0.13	0.31	0.09	0.03	0.95	0.04	0.04	0.00	0.13	0.65	0.08	0.08	0.22	0.09	0.13	0.07	0.09	0.38	311
Russia_Moscow State University of Design and Technology (MSUDT)	0.09	0.11	0.09	0.04	0.26	0.01	0.10	0.00	0.13	0.40	0.02	0.21	0.18	0.07	0.11	0.07	0.10	0.20	401
Russia_Financial University under the Government of the Russian Federation	0.15	0.19	0.90	0.05	0.09	0.18	0.09	0.91	0.08	0.40	0.06	0.93	0.37	0.23	0.36	0.15	0.13	0.59	208
Russia_Mordovia State University	0.12	0.15	0.29	0.09	0.13	0.08	0.09	0.51	0.09	0.52	0.05	0.43	0.26	0.10	0.14	0.14	0.28	0.35	333
Russia_RUDN University	0.93	0.97	0.33	0.14	0.83	0.14	0.16	0.44	0.26	0.89	0.37	0.43	0.49	0.25	0.41	0.19	0.15	0.89	24
Russia_Mendeleyev University of Chemical Technology	0.37	0.56	0.40	0.19	0.54	0.06	0.27	0.35	0.04	0.16	0.04	0.21	0.09	0.18	0.27	0.42	0.72	0.48	265
China_Beijing University of Technology	0.33	0.46	0.24	0.36	0.53	0.32	0.41	0.40	0.15	0.27	0.12	0.43	0.23	0.54	0.69	0.75	0.76	0.73	117
Russia_Bashkir State University	0.19	0.26	0.13	0.15	0.42	0.08	0.16	0.10	0.03	0.20	0.06	0.08	0.08	0.07	0.11	0.16	0.43	0.28	371
China_Southeast University	0.48	0.71	0.40	0.58	0.36	0.58	0.66	0.31	0.45	0.36	0.18	0.38	0.34	0.45	0.63	0.88	0.96	0.88	26
Russia_Volgograd State University	0.18	0.20	0.00	0.10	0.39	0.03	0.12	0.00	0.14	0.19	0.08	0.08	0.11	0.07	0.11	0.09	0.19	0.21	395
Switzerland_University of St. Gallen	0.52	0.75	0.40	0.21	0.67	0.53	0.21	0.40	0.97	0.93	0.85	0.30	0.78	0.32	0.48	0.30	0.29	0.89	25
Hungary_University of Debrecen	0.20	0.40	0.19	0.32	0.29	0.55	0.26	0.00	0.43	0.72	0.72	0.18	0.51	0.41	0.58	0.33	0.26	0.69	154
USA_American University	0.86	0.90	0.46	0.33	0.45	0.98	0.25	0.31	0.40	0.57	0.17	0.48	0.40	0.65	0.78	0.22	0.07	0.82	61
Russia_Irkutsk State University	0.08	0.09	0.24	0.13	0.09	0.15	0.13	0.15	0.15	0.24	0.28	0.08	0.17	0.06	0.10	0.10	0.27	0.29	366
Russia_Plekhanov Russian University of Economics	0.32	0.26	0.19	0.06	0.47	0.07	0.07	0.25	0.44	0.43	0.10	0.26	0.30	0.24	0.35	0.11	0.08	0.41	304
Iraq_Jabir Ibn Hayyan Medical University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.99	0.98	0.99	0.62	0.30	364
Taiwan_National Taiwan Normal University	0.46	0.55	0.63	0.33	0.33	0.20	0.42	0.61	0.54	0.82	0.26	0.32	0.49	0.46	0.62	0.93	0.99	0.89	23
Republic of Korea_Gwangju Institute of Science and Technology	0.94	0.99	0.19	0.93	0.19	0.41	0.98	0.40	0.44	0.31	0.40	0.08	0.30	0.95	0.94	0.99	0.87	1.00	1
Taiwan_Kaohsiung Medical University	0.26	0.33	0.24	0.70	0.48	0.22	0.90	0.25	0.33	0.39	0.15	0.53	0.35	0.47	0.62	0.66	0.66	0.76	95
Poland_Lodz University of Technology	0.13	0.20	0.13	0.26	0.17	0.16	0.32	0.15	0.15	0.22	0.22	0.08	0.16	0.19	0.27	0.25	0.34	0.33	345
Russia_Orel State University	0.18	0.24	0.70	0.03	0.41	0.04	0.03	0.74	0.00	0.20	0.20	0.70	0.27	0.05	0.06	0.20	0.71	0.53	247
USA_Marquette University	0.89	0.86	0.33	0.28	0.10	0.31	0.31	0.20	0.31	0.28	0.14	0.28	0.24	0.58	0.70	0.20	0.07	0.70	139
Taiwan_Chang Gung University	0.34	0.47	0.33	0.61	0.43	0.22	0.82	0.44	0.27	0.27	0.11	0.53	0.29	0.57	0.70	0.66	0.85	0.82	60
Russia_Don State Technical University	0.23	0.17	0.00	0.06	0.52	0.08	0.06	0.10	0.08	0.48	0.44	0.18	0.29	0.08	0.12	0.09	0.15	0.34	340
Spain_University of Rovira i Virgili	0.58	0.65	0.24	0.65	0.41	0.59	0.60	0.25	0.40	0.51	0.56	0.35	0.46	0.18	0.25	0.36	0.64	0.80	68
Russia_Northern (Arctic) Federal University (NArFU)	0.23	0.21	0.00	0.07	0.62	0.05	0.09	0.00	0.20	0.23	0.04	0.08	0.12	0.12	0.15	0.18	0.35	0.26	382
Azerbaijan_Baku State University	0.15	0.17	0.13	0.10	0.22	0.09	0.10	0.31	0.23	0.13	0.71	0.43	0.37	0.02	0.03	0.07	0.62	0.42	295
Thailand_Thammasat University	0.10	0.10	0.29	0.16	0.92	0.21	0.15	0.25	0.57	0.09	0.45	0.21	0.32	0.58	0.70	0.45	0.30	0.55	232
China_Renmin University of China	0.79	0.88	0.36	0.26	0.58	0.43	0.25	0.40	0.48	0.32	0.45	0.32	0.39	0.67	0.77	0.38	0.18	0.71	135
Iraq_Al-Noor University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.06	0.08	0.12	0.30	0.09	416
Kazakhstan_EA Buketov Karaganda State University	0.05	0.05	0.00	0.04	0.07	0.04	0.08	0.00	0.06	0.09	0.36	0.08	0.13	0.04	0.06	0.06	0.15	0.14	411
Hungary_University of Szeged	0.32	0.52	0.29	0.38	0.38	0.49	0.34	0.20	0.39	0.67	0.64	0.24	0.49	0.41	0.57	0.31	0.24	0.73	121
Russia_Saint-Petersburg State Electotechnical University LETI	0.20	0.34	0.49	0.14	0.46	0.07	0.17	0.40	0.05	0.73	0.23	0.53	0.38	0.17	0.23	0.42	0.80	0.64	179
Russia_Samara University	0.09	0.12	0.19	0.16	0.09	0.07	0.16	0.25	0.05	0.14	0.21	0.35	0.18	0.10	0.13	0.21	0.53	0.29	367
Iraq_Al-Kitab University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.04	0.05	0.01	0.01	0.03	430
USA_Worcester Polytechnic Institute	0.29	0.34	0.33	0.41	0.24	0.48	0.41	0.20	0.62	0.79	0.43	0.28	0.53	0.65	0.75	0.42	0.22	0.74	105
India_University of Hyderabad	0.90	0.96	0.51	0.47	0.35	0.22	0.57	0.40	0.00	0.06	0.11	0.21	0.08	0.04	0.05	0.28	0.97	0.67	163
Poland_Warsaw University of Technology	0.21	0.34	0.53	0.22	0.25	0.32	0.20	0.61	0.15	0.33	0.47	0.48	0.35	0.16	0.21	0.24	0.71	0.60	203
China_Hangzhou Dianzi University	0.00	0.00	0.13	0.29	0.00	0.52	0.27	0.15	0.29	0.04	0.14	0.30	0.18	0.19	0.24	0.30	0.45	0.30	363
Spain_University of Alcala	0.21	0.31	0.49	0.29	0.06	0.43	0.26	0.51	0.53	0.72	0.54	0.32	0.53	0.19	0.25	0.35	0.73	0.59	209
Ukraine_Ostrogradskiy National University of Kremenchuk	0.04	0.04	0.49	0.02	0.03	0.02	0.03	0.54	0.21	0.03	0.44	0.48	0.29	0.03	0.04	0.03	0.06	0.27	374
Canada_University of Sherbrooke	0.75	0.78	0.13	0.37	0.51	0.45	0.33	0.25	0.77	0.38	0.50	0.28	0.48	0.46	0.59	0.37	0.48	0.81	63
Norway_University of Tromso	0.27	0.42	0.36	0.48	0.43	0.70	0.40	0.40	0.65	0.49	0.91	0.43	0.63	0.39	0.52	0.35	0.44	0.84	49
Tunisia_Universite de la Manouba	0.24	0.35	0.00	0.17	0.04	0.16	0.17	0.00	0.14	0.07	0.83	0.08	0.27	0.05	0.07	0.03	0.03	0.32	352
Ukraine_South Ukrainian National Pedagogical University named after K.D. Ushynsky	0.33	0.32	0.13	0.05	0.09	0.07	0.06	0.25	0.18	0.28	0.96	0.24	0.41	0.03	0.03	0.04	0.12	0.42	296
Russia_Tyumen State University	0.13	0.16	0.09	0.13	0.12	0.23	0.14	0.10	0.26	0.33	0.62	0.08	0.32	0.18	0.22	0.32	0.52	0.42	298
Japan_Yokohama National University	0.35	0.43	0.43	0.30	0.91	0.21	0.32	0.40	0.51	0.35	0.17	0.38	0.35	0.26	0.35	0.64	0.87	0.75	103
Japan_Tokyo Metropolitan University	0.39	0.45	0.33	0.79	0.87	0.99	0.53	0.51	0.34	0.25	0.53	0.56	0.42	0.38	0.49	0.34	0.36	0.82	57
Russia_Belgorod National Research University	0.30	0.25	0.19	0.15	0.15	0.32	0.14	0.15	0.21	0.72	0.52	0.08	0.38	0.14	0.16	0.35	0.73	0.61	189
India_Amity University	0.07	0.08	0.55	0.15	0.04	0.21	0.14	0.60	0.11	0.26	0.21	0.66	0.31	0.22	0.28	0.06	0.05	0.46	276
Lebanon_Lebanese American University	0.36	0.36	0.24	0.23	0.62	0.35	0.20	0.00	0.91	0.73	0.82	0.21	0.67	0.73	0.80	0.11	0.02	0.76	96
China_Beijing Jiaotong University	0.37	0.52	0.40	0.39	0.24	0.41	0.43	0.40	0.28	0.37	0.28	0.53	0.36	0.41	0.53	0.69	0.77	0.77	83
Iraq_University of Kufa	0.11	0.11	0.43	0.08	0.06	0.12	0.06	0.54	0.06	0.00	0.97	0.53	0.39	0.24	0.31	0.15	0.13	0.43	290
Mexico_National Autonomous University of Mexico	0.22	0.29	0.87	0.26	0.40	0.24	0.24	0.85	0.49	0.34	0.51	0.86	0.56	0.38	0.50	0.61	0.73	0.90	21
Egypt_American University in Cairo	0.08	0.08	0.51	0.23	0.98	0.23	0.26	0.31	0.95	0.29	0.73	0.48	0.62	0.97	0.96	0.38	0.04	0.93	11
China_Jinan University	0.32	0.37	0.13	0.34	0.68	0.42	0.34	0.15	0.48	0.92	0.14	0.21	0.43	0.64	0.71	0.46	0.32	0.68	161
Iceland_University of Iceland	0.30	0.28	0.29	0.79	0.40	0.90	0.63	0.44	0.50	0.57	0.97	0.43	0.63	0.28	0.36	0.71	0.95	0.91	16
United Arab Emirates_American University of Sharjah	0.00	0.00	0.33	0.28	0.00	0.25	0.31	0.20	1.00	1.00	0.84	0.18	0.77	0.86	0.86	0.10	0.02	0.73	122
Taiwan_Tunghai University	0.06	0.06	0.00	0.19	0.15	0.14	0.19	0.00	0.41	0.36	0.17	0.08	0.25	0.15	0.17	0.22	0.37	0.29	365
USA_Hofstra University	0.90	0.89	0.29	0.50	0.68	0.83	0.34	0.54	0.21	0.47	0.22	0.48	0.34	0.70	0.76	0.05	0.01	0.82	56
Spain_Polytechnic University of Madrid	0.35	0.40	0.70	0.30	0.22	0.35	0.31	0.64	0.17	0.61	0.54	0.53	0.46	0.18	0.21	0.29	0.56	0.74	108
China_Wuhan University of Technology	0.17	0.18	0.33	0.29	0.21	0.86	0.23	0.57	0.21	0.18	0.30	0.48	0.29	0.45	0.54	0.41	0.46	0.59	214
Thailand_Chulalongkorn University	0.41	0.50	0.78	0.34	0.56	0.35	0.32	0.68	0.45	0.20	0.62	0.32	0.39	0.76	0.80	0.54	0.26	0.79	74
Russia_Voronezh State Technical University	0.06	0.07	0.13	0.05	0.09	0.04	0.06	0.15	0.04	0.18	0.17	1.00	0.34	0.00	0.00	0.01	0.30	0.25	385
Russia_Immanuel Kant Baltic Federal University	0.22	0.27	0.19	0.14	0.09	0.11	0.15	0.20	0.17	0.27	0.61	0.08	0.27	0.15	0.17	0.15	0.26	0.35	334
Poland_University of Lodz	0.18	0.26	0.09	0.22	0.34	0.20	0.23	0.15	0.19	0.26	0.30	0.21	0.23	0.08	0.10	0.14	0.32	0.37	325
Taiwan_National Sun Yat-Sen University	0.47	0.63	0.36	0.56	0.44	0.24	0.79	0.44	0.35	0.32	0.30	0.53	0.37	0.42	0.52	0.87	0.97	0.84	47
China_Sichuan University	0.56	0.67	0.40	0.54	0.31	0.37	0.63	0.35	0.45	0.21	0.08	0.53	0.31	0.39	0.48	0.70	0.82	0.81	64
Iraq_University of Ahl al-Bayt	0.00	0.00	0.00	0.18	0.00	0.13	0.16	0.00	0.00	0.00	0.67	0.08	0.17	0.09	0.11	0.15	0.58	0.18	403
Russia_Samara State Technical University	0.11	0.14	0.13	0.11	0.15	0.06	0.12	0.15	0.05	0.12	0.02	0.24	0.09	0.13	0.14	0.26	0.58	0.26	381
China_Wuhan University of Science & Technology	0.09	0.09	0.09	0.20	0.27	0.34	0.20	0.10	0.25	0.07	0.09	0.21	0.14	0.14	0.15	0.28	0.55	0.32	349
Iraq_University of Babylon	0.19	0.16	0.09	0.08	0.20	0.37	0.05	0.10	0.03	0.02	0.97	0.08	0.27	0.16	0.17	0.08	0.17	0.38	313
China_Northwest University, Xi’an	0.30	0.37	0.53	0.38	0.33	0.47	0.34	0.35	0.12	0.19	0.10	0.67	0.26	0.27	0.33	0.36	0.57	0.62	187
Iraq_University of Tikrit	0.27	0.31	0.00	0.11	0.22	0.27	0.05	0.00	0.00	0.02	0.99	0.08	0.26	0.01	0.01	0.00	0.00	0.33	344
Puerto Rico_University of Puerto Rico	0.15	0.22	0.49	0.29	0.78	0.73	0.21	0.44	0.16	0.05	0.56	0.30	0.26	0.13	0.13	0.17	0.32	0.57	218
Iraq_University of Anbar	0.18	0.22	0.00	0.09	0.80	0.29	0.07	0.00	0.05	0.00	0.98	0.08	0.27	0.15	0.16	0.12	0.14	0.38	312
USA_East Carolina University	0.39	0.39	0.13	0.28	0.51	0.38	0.27	0.15	0.59	0.12	0.21	0.24	0.28	0.59	0.65	0.27	0.11	0.51	256
China_Northeastern University (China)	0.45	0.55	0.13	0.34	0.34	0.39	0.44	0.40	0.79	0.24	0.12	0.53	0.42	0.58	0.65	0.86	0.87	0.75	98
USA_Texas Christian University	0.44	0.40	0.24	0.29	0.96	0.40	0.25	0.10	0.30	0.27	0.18	0.35	0.27	0.81	0.82	0.18	0.04	0.57	220
Iraq_Al-Maarif University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.07	0.08	0.10	0.22	0.06	424
Russia_Ufa State Petroleum Technological University (USPTU)	0.04	0.04	0.13	0.05	0.05	0.02	0.09	0.10	0.12	0.33	0.02	0.08	0.13	0.09	0.10	0.19	0.44	0.27	377
China_Xiamen University	0.40	0.56	0.40	0.49	0.19	0.58	0.43	0.35	0.36	0.25	0.32	0.26	0.29	0.62	0.67	0.67	0.69	0.79	73
Brazil_Federal University of Vicosa	0.69	0.82	0.40	0.38	0.81	0.12	0.54	0.31	0.19	0.13	0.13	0.48	0.23	0.40	0.47	0.24	0.14	0.57	221
Russia_Southwest State University	0.29	0.29	0.00	0.08	0.39	0.09	0.08	0.10	0.10	0.28	0.23	0.08	0.16	0.06	0.07	0.25	0.74	0.30	359
Slovenia_University of Ljubljana	0.34	0.47	0.60	0.40	0.30	0.43	0.40	0.63	0.29	0.33	0.64	0.56	0.46	0.22	0.25	0.31	0.54	0.75	104
China_Northeast Normal University (China)	0.56	0.63	0.00	0.35	0.65	0.48	0.30	0.10	0.22	0.11	0.07	0.08	0.10	0.42	0.50	0.18	0.09	0.57	219
Spain_University of the Basque Country	0.54	0.62	0.29	0.49	0.86	0.49	0.45	0.25	0.09	0.25	0.68	0.35	0.34	0.24	0.28	0.27	0.34	0.70	136
Poland_Gdansk University of Technology	0.25	0.22	0.19	0.29	0.64	0.26	0.32	0.15	0.15	0.21	0.26	0.08	0.16	0.24	0.28	0.33	0.41	0.46	273
Russia_Tver State University	0.03	0.27	0.09	0.11	0.73	0.05	0.13	0.10	0.06	0.16	0.20	0.08	0.11	0.06	0.07	0.67	1.00	0.37	326
Republic of Korea_Yeungnam University	0.30	0.23	0.19	0.44	0.28	0.38	0.50	0.20	0.56	0.29	0.27	0.30	0.35	0.36	0.43	0.41	0.46	0.57	222
Russia_Tomsk State University of Control Systems and Radioelectronics (TUSUR University)	0.21	0.26	0.19	0.15	0.17	0.27	0.15	0.31	0.23	0.77	0.32	0.28	0.40	0.22	0.24	0.58	0.89	0.48	266
Taiwan_National Chung Cheng University	0.26	0.32	0.19	0.29	0.25	0.15	0.38	0.31	0.15	0.26	0.13	0.32	0.20	0.18	0.19	0.57	0.88	0.47	271
Spain_University of Santiago de Compostela	0.36	0.46	0.49	0.41	0.18	0.49	0.37	0.54	0.14	0.44	0.72	0.53	0.46	0.24	0.26	0.32	0.62	0.75	102
Russia_Volgograd State Technical University	0.09	0.10	0.00	0.09	0.16	0.02	0.11	0.00	0.03	0.36	0.03	0.08	0.11	0.10	0.11	0.25	0.58	0.27	376
Finland_University of Jyvaskyla	0.57	0.66	0.36	0.47	0.79	0.58	0.45	0.40	0.43	0.28	0.86	0.38	0.49	0.37	0.44	0.63	0.94	0.94	9
Slovenia_University of Maribor	0.19	0.25	0.19	0.35	0.15	0.38	0.39	0.15	0.17	0.28	0.54	0.08	0.26	0.18	0.18	0.29	0.50	0.54	237
Iraq_University of Misan	0.00	0.00	0.00	0.06	0.00	0.09	0.05	0.00	0.00	0.00	1.00	0.08	0.26	0.17	0.18	0.05	0.03	0.17	405
China_Yangzhou University	0.11	0.12	0.00	0.28	0.22	0.45	0.28	0.00	0.27	0.17	0.10	0.08	0.14	0.28	0.32	0.39	0.52	0.45	281
Japan_University of Electro-Communications	0.39	0.46	0.24	0.42	0.56	0.19	0.55	0.31	0.49	0.30	0.41	0.32	0.38	0.36	0.43	0.48	0.56	0.70	141
Spain_ESIC Business and Marketing School	0.00	0.00	0.00	0.04	0.00	0.10	0.04	0.00	0.73	0.58	0.29	0.08	0.42	0.28	0.33	0.06	0.04	0.38	316
Taiwan_National Chung Hsing University	0.38	0.48	0.40	0.36	0.62	0.20	0.41	0.57	0.33	0.27	0.12	0.48	0.29	0.36	0.42	0.60	0.87	0.70	143
UK_Swansea University	0.37	0.31	0.40	0.53	0.36	0.86	0.45	0.40	0.81	0.79	0.77	0.53	0.74	0.42	0.48	0.41	0.45	0.95	6
China_Yanshan University	0.20	0.23	0.00	0.24	0.58	0.33	0.24	0.00	0.24	0.06	0.06	0.08	0.09	0.23	0.24	0.45	0.76	0.46	275
Iraq_Iraq University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.57	0.00	0.00	0.08	0.15	0.08	0.09	0.04	0.05	0.15	409
Azerbaijan_Azerbaijan University of Architecture and Construction	0.17	0.15	0.00	0.02	0.73	0.03	0.03	0.10	0.24	0.43	0.44	0.08	0.29	0.05	0.06	0.03	0.03	0.32	350
Thailand_Chiang Mai University	0.22	0.23	0.55	0.24	0.26	0.18	0.26	0.35	0.19	0.12	0.55	0.30	0.28	0.74	0.76	0.63	0.35	0.63	180
China_Shenzhen University	0.05	0.06	0.09	0.31	0.11	0.66	0.29	0.00	0.37	0.06	0.25	0.08	0.18	0.72	0.73	0.61	0.48	0.42	293
Iraq_Uruk University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.16	0.00	0.00	0.08	0.04	0.01	0.01	0.02	0.30	0.04	429
China_East China University of Science and Technology	0.49	0.55	0.53	0.68	0.44	0.51	0.69	0.40	0.07	0.11	0.11	0.48	0.18	0.45	0.50	0.62	0.61	0.80	69
China_Nanjing University of Aeronautics & Astronautics	0.39	0.46	0.19	0.42	0.25	0.47	0.49	0.25	0.28	0.18	0.09	0.21	0.17	0.49	0.54	0.85	0.92	0.74	107
Nigeria_University of Ibadan	0.60	0.74	0.61	0.25	0.56	0.61	0.21	0.51	0.51	0.09	0.60	0.32	0.38	0.11	0.11	0.15	0.31	0.63	181
China_Dalian University of Technology	0.51	0.57	0.36	0.55	0.36	0.49	0.60	0.44	0.60	0.14	0.16	0.48	0.34	0.44	0.49	0.76	0.89	0.82	58
China_China Pharmaceutical University	0.42	0.45	0.36	0.34	0.50	0.39	0.32	0.25	0.10	0.13	0.04	0.26	0.12	0.40	0.44	0.34	0.53	0.52	251
Croatia_University of Rijeka	0.15	0.25	0.00	0.20	0.12	0.26	0.19	0.15	0.07	0.04	0.58	0.08	0.18	0.12	0.12	0.08	0.18	0.27	380
Japan_Waseda University	0.28	0.24	0.82	0.32	0.47	0.42	0.27	0.78	0.58	0.51	0.41	0.62	0.53	0.37	0.42	0.33	0.30	0.78	78
USA_Oklahoma State University	0.55	0.46	0.36	0.56	0.88	0.67	0.53	0.25	0.70	0.39	0.42	0.26	0.44	0.70	0.71	0.48	0.21	0.85	37
Thailand_Prince of Songkla University	0.16	0.13	0.40	0.21	0.81	0.20	0.20	0.47	0.33	0.12	0.49	0.43	0.34	0.42	0.45	0.18	0.08	0.46	277
Taiwan_National Taipei University of Technology	0.35	0.35	0.36	0.33	0.26	0.25	0.37	0.54	0.46	0.42	0.09	0.48	0.36	0.57	0.59	0.73	0.89	0.75	100
China_Nanjing Agricultural University	0.55	0.53	0.00	0.55	0.50	0.45	0.58	0.00	0.27	0.13	0.14	0.08	0.14	0.41	0.44	0.71	0.82	0.62	188
Russia_Omsk State Technical University	0.17	0.19	0.09	0.07	0.75	0.06	0.09	0.00	0.04	0.74	0.10	0.18	0.26	0.07	0.07	0.16	0.41	0.37	324
UK_University of Portsmouth	0.21	0.15	0.13	0.45	0.49	0.88	0.31	0.20	0.84	0.83	0.91	0.24	0.71	0.28	0.30	0.12	0.07	0.72	129
China_Chongqing University	0.47	0.51	0.13	0.44	0.44	0.46	0.49	0.10	0.35	0.22	0.17	0.21	0.23	0.45	0.48	0.61	0.62	0.68	158
Turkey_Ege University	0.19	0.30	0.00	0.26	0.30	0.16	0.23	0.00	0.22	0.18	0.14	0.08	0.14	0.40	0.43	0.28	0.33	0.37	322
UK_University of Central Lancashire	0.14	0.11	0.19	0.28	0.27	0.43	0.25	0.31	0.65	0.70	0.65	0.56	0.65	0.29	0.32	0.11	0.07	0.59	210
Spain_University of Vigo	0.30	0.35	0.36	0.34	0.11	0.39	0.35	0.20	0.14	0.27	0.62	0.56	0.40	0.25	0.26	0.24	0.38	0.58	217
China_Nanjing University of Science & Technology	0.42	0.51	0.09	0.33	0.45	0.60	0.31	0.20	0.89	0.19	0.10	0.28	0.36	1.00	1.00	1.00	0.48	0.84	48
Mexico_Monterrey Institute of Technology and Higher Education	0.28	0.30	0.53	0.26	0.47	0.32	0.27	0.35	0.59	0.52	0.69	0.56	0.60	0.43	0.46	0.57	0.62	0.77	89
Japan_Kyushu Institute of Technology	0.41	0.40	0.46	0.46	0.81	0.28	0.54	0.31	0.46	0.22	0.32	0.60	0.40	0.33	0.38	0.39	0.40	0.69	152
USA_University of Memphis	0.62	0.54	0.13	0.31	0.77	0.38	0.35	0.15	0.32	0.16	0.29	0.26	0.25	0.55	0.56	0.63	0.54	0.67	164
Iraq_Islamic University in Najaf	0.03	0.03	0.00	0.02	0.04	0.00	0.01	0.00	0.00	0.00	0.00	0.08	0.00	0.21	0.20	0.04	0.02	0.06	422
Russia_Siberian Federal University	0.56	0.63	0.19	0.16	0.50	0.10	0.18	0.25	0.63	0.22	0.20	0.24	0.31	0.37	0.41	0.57	0.62	0.54	236
Iraq_University of Diyala	0.14	0.14	0.00	0.06	0.42	0.30	0.04	0.00	0.00	0.00	0.98	0.08	0.26	0.02	0.02	0.03	0.17	0.22	393
China_University of Electronic Science and Technology of China	0.40	0.44	0.00	0.48	0.24	0.54	0.59	0.15	0.26	0.16	0.31	0.18	0.22	0.45	0.47	0.77	0.89	0.72	127
USA_New Mexico State University	0.38	0.33	0.19	0.49	0.88	0.54	0.43	0.20	0.39	0.43	0.49	0.28	0.39	0.66	0.66	0.69	0.54	0.79	75
Czech Republic_University of West Bohemia	0.25	0.34	0.24	0.19	0.16	0.12	0.23	0.15	0.36	0.23	0.69	0.43	0.43	0.26	0.26	0.62	0.91	0.61	195
China_China Medical University (Taiwan)	0.22	0.21	0.19	0.86	0.14	0.30	0.97	0.20	0.23	0.41	0.21	0.21	0.25	0.99	0.97	0.79	0.14	0.61	191
UK_University of Plymouth	0.36	0.23	0.40	0.51	1.00	0.80	0.42	0.31	0.69	0.62	0.75	0.48	0.64	0.36	0.40	0.21	0.14	0.93	12
Portugal_Aveiro University	0.66	0.68	0.49	0.79	0.15	0.42	0.89	0.47	0.36	0.55	0.77	0.32	0.50	0.26	0.25	0.44	0.77	0.77	87
USA_Stevens Institute of Technology	0.42	0.55	0.29	0.34	0.45	0.38	0.36	0.20	0.66	0.95	0.54	0.28	0.61	0.76	0.75	0.52	0.26	0.85	40
Turkey_Atilim University	0.08	0.09	0.13	0.19	0.38	0.32	0.21	0.10	0.29	0.25	0.51	0.28	0.33	0.21	0.19	0.16	0.18	0.41	301
Iraq_Al-Mustaqbal University College	0.00	0.00	0.00	0.08	0.00	0.23	0.05	0.00	0.22	0.00	0.98	0.08	0.32	0.16	0.15	0.20	0.30	0.29	369
Romania_George Emil Palade University of Medicine, Pharmacy, Science, and Technology of Targu Mures	0.17	0.21	0.00	0.17	0.27	0.12	0.16	0.00	0.11	0.35	0.25	0.08	0.18	0.14	0.13	0.04	0.06	0.26	383
Turkey_TOBB University of Economics and Technology	0.07	0.10	0.09	0.59	0.05	0.92	0.40	0.10	0.18	0.05	0.88	0.21	0.33	0.24	0.22	0.17	0.15	0.53	246
China_Ningbo University	0.05	0.06	0.00	0.39	0.17	0.40	0.39	0.00	0.25	0.30	0.07	0.08	0.16	0.34	0.37	0.42	0.45	0.43	288
UK_Coventry University	0.14	0.11	0.36	0.20	0.41	0.43	0.19	0.44	0.85	0.98	0.64	0.68	0.80	0.31	0.33	0.17	0.12	0.69	149
Republic of Korea_Chonnam National University	0.52	0.44	0.40	0.61	0.19	0.35	0.70	0.31	0.30	0.33	0.27	0.56	0.36	0.49	0.51	0.72	0.79	0.86	32
Taiwan_National Taipei University	0.15	0.12	0.29	0.19	0.28	0.22	0.23	0.31	0.17	0.22	0.18	0.48	0.26	0.23	0.21	0.25	0.29	0.42	297
Russia_Moscow State Institute of Radio Engineering, Electrical & Automation	0.07	0.07	0.74	0.14	0.05	0.06	0.17	0.73	0.07	0.16	0.09	0.70	0.25	0.21	0.18	0.44	0.73	0.52	248
Republic of Korea_Sejong University	0.45	0.36	0.33	0.52	0.89	0.54	0.56	0.20	0.54	0.50	0.36	0.43	0.46	0.34	0.37	0.70	0.84	0.91	18
UK_Middlesex University	0.34	0.23	0.24	0.24	0.65	0.67	0.24	0.25	0.87	0.98	0.61	0.60	0.78	0.33	0.36	0.12	0.07	0.83	51
China_Nanjing Normal University	0.29	0.33	0.09	0.40	0.33	0.54	0.34	0.00	0.22	0.30	0.15	0.08	0.17	0.29	0.29	0.49	0.60	0.56	225
Russia_South Ural State University	0.09	0.09	0.19	0.11	0.08	0.11	0.11	0.15	0.11	0.30	0.22	0.18	0.19	0.11	0.09	0.23	0.54	0.30	358
China_Xidian University	0.38	0.41	0.51	0.27	0.50	0.39	0.33	0.57	0.13	0.15	0.08	0.56	0.22	0.45	0.45	0.71	0.90	0.74	111
New Zealand_Auckland University of Technology	0.30	0.21	0.40	0.39	0.61	0.94	0.28	0.20	0.96	0.99	0.88	0.38	0.82	0.27	0.25	0.12	0.08	0.90	22
Japan_Hitotsubashi University	0.45	0.46	0.51	0.16	0.21	0.20	0.20	0.57	0.53	0.57	0.44	0.43	0.49	0.33	0.36	0.40	0.41	0.69	148
Brazil_Universidade Federal do Ceara	0.54	0.73	0.24	0.27	0.36	0.26	0.30	0.15	0.25	0.07	0.30	0.21	0.19	0.40	0.41	0.27	0.19	0.60	204
Iraq_University of Thi-Qar	0.09	0.10	0.00	0.10	0.12	0.24	0.06	0.00	0.00	0.00	0.96	0.08	0.25	0.12	0.10	0.12	0.33	0.30	361
Iraq_University College in Baghdad Iraq	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.10	0.09	0.07	0.12	0.04	428
Russia_Tomsk State University of Architecture and Building	0.07	0.08	0.00	0.08	0.89	0.04	0.11	0.15	0.10	0.65	0.07	0.08	0.21	0.00	0.00	0.00	0.38	0.30	360
Iraq_Al-Nisour University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.22	0.00	0.00	0.08	0.06	0.03	0.03	0.07	0.43	0.05	426
UK_Northumbria University	0.29	0.17	0.36	0.34	0.79	0.86	0.29	0.35	0.69	0.68	0.74	0.35	0.62	0.30	0.30	0.09	0.06	0.66	167
Romania_University of Bucharest	0.43	0.41	0.61	0.25	0.39	0.18	0.28	0.44	0.14	0.13	0.49	0.48	0.30	0.11	0.09	0.19	0.43	0.56	227
Egypt_Ain Shams University	0.30	0.30	0.43	0.15	0.06	0.37	0.11	0.10	0.43	0.16	0.57	0.60	0.44	0.10	0.08	0.05	0.10	0.43	285
Spain_University of Salamanca	0.58	0.56	0.53	0.41	0.24	0.47	0.34	0.44	0.18	0.67	0.55	0.35	0.44	0.20	0.17	0.23	0.34	0.73	118
Russia_Voronezh Institute of High Technologies	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.19	0.00	0.08	0.05	0.05	0.04	0.17	0.54	0.16	408
UK_Oxford Brookes University	0.24	0.18	0.79	0.25	1.00	0.48	0.25	0.79	0.76	0.84	0.62	0.85	0.78	0.37	0.37	0.10	0.05	0.84	46
India_Vellore Institute of Technology	0.39	0.44	0.19	0.25	0.10	0.25	0.00	0.15	0.56	0.15	0.00	0.08	0.19	0.35	0.34	0.14	0.11	0.36	329
Romania_West University of Timisoara	0.29	0.17	0.19	0.40	0.17	0.87	0.26	0.15	0.09	0.24	0.74	0.08	0.28	0.11	0.08	0.10	0.14	0.45	278
Taiwan_National Dong Hwa University	0.19	0.18	0.00	0.33	0.49	0.23	0.39	0.00	0.30	0.44	0.39	0.08	0.30	0.30	0.27	0.75	0.93	0.53	245
New Zealand_University of Waikato	0.38	0.26	0.33	0.48	0.64	0.58	0.46	0.25	0.89	0.87	0.83	0.28	0.73	0.38	0.37	0.37	0.36	0.88	27
Taiwan_Chung Shan Medical University	0.25	0.18	0.09	0.57	0.56	0.27	0.71	0.15	0.13	0.29	0.03	0.21	0.15	0.30	0.29	0.39	0.55	0.50	260
USA_Old Dominion University	0.54	0.41	0.43	0.42	0.97	0.65	0.39	0.35	0.41	0.17	0.45	0.53	0.39	0.69	0.64	0.43	0.20	0.91	17
Russia_Pacific National University	0.09	0.07	0.00	0.04	0.18	0.03	0.07	0.00	0.09	0.30	0.15	0.08	0.14	0.09	0.07	0.14	0.25	0.17	406
UK_University of Westminster	0.16	0.12	0.49	0.23	0.96	0.33	0.25	0.51	0.86	0.99	0.34	0.69	0.73	0.34	0.34	0.09	0.04	0.83	53
Pakistan_NED University of Engineering and Technology	0.04	0.03	0.00	0.15	0.08	0.23	0.12	0.00	0.04	0.03	0.97	0.08	0.27	0.09	0.07	0.10	0.17	0.29	368
USA_Portland State University	0.26	0.15	0.36	0.30	0.00	0.41	0.32	0.35	0.68	0.44	0.24	0.38	0.43	0.60	0.55	0.45	0.31	0.61	190
Russia_North Caucasus Federal University	0.19	0.18	0.00	0.06	0.25	0.05	0.07	0.00	0.55	0.34	0.17	0.08	0.27	0.13	0.09	0.13	0.21	0.24	388
UK_University of Ulster	0.33	0.20	0.29	0.35	0.72	0.48	0.34	0.31	0.93	0.45	0.81	0.48	0.68	0.31	0.28	0.33	0.36	0.72	128
USA_Florida Atlantic University	0.43	0.28	0.24	0.27	0.82	0.38	0.27	0.15	0.66	0.52	0.34	0.30	0.46	0.52	0.46	0.38	0.25	0.64	175
USA_Savannah College of Art and Design	0.00	0.00	0.00	0.02	0.00	0.01	0.08	0.00	0.52	0.85	0.02	0.08	0.36	0.68	0.61	0.82	0.70	0.50	259
USA_Oakland University	0.53	0.37	0.33	0.33	0.46	0.40	0.35	0.25	0.39	0.20	0.34	0.35	0.31	0.55	0.49	0.13	0.04	0.56	223
Croatia_University of Zagreb	0.34	0.51	0.46	0.26	0.32	0.27	0.28	0.40	0.12	0.15	0.54	0.24	0.25	0.17	0.14	0.15	0.25	0.48	270
UK_University of the West of England	0.21	0.12	0.43	0.25	0.89	0.51	0.25	0.40	0.67	0.76	0.46	0.38	0.57	0.33	0.31	0.18	0.10	0.70	145
Switzerland_University of Lucerne	0.53	0.67	0.29	0.21	0.78	0.66	0.22	0.35	0.87	0.62	0.76	0.43	0.68	0.39	0.36	0.23	0.25	0.84	41
Turkey_Ankara University	0.32	0.45	0.79	0.21	0.25	0.27	0.20	0.77	0.20	0.24	0.26	0.79	0.37	0.77	0.69	0.58	0.44	0.75	99
Hungary_Eotvos Lorand University	0.40	0.41	0.36	0.44	0.18	0.73	0.37	0.35	0.53	0.49	0.87	0.28	0.54	0.34	0.32	0.58	0.71	0.84	43
USA_Mississippi State University	0.39	0.35	0.29	0.52	0.94	0.40	0.55	0.20	0.35	0.19	0.20	0.32	0.26	0.39	0.35	0.57	0.60	0.74	112
Russia_Ulyanovsk State University	0.10	0.11	0.00	0.13	0.04	0.08	0.15	0.00	0.06	0.44	0.22	0.08	0.19	0.11	0.08	0.20	0.47	0.21	394
Russia_Novosibirsk State University of Economics and Management	0.06	0.05	0.00	0.02	0.08	0.06	0.04	0.00	0.05	0.17	0.02	0.08	0.06	0.00	0.00	0.00	0.08	0.07	419
Taiwan_Yuan Ze University	0.22	0.16	0.29	0.38	0.28	0.17	0.52	0.31	0.34	0.42	0.10	0.30	0.28	0.38	0.34	0.51	0.50	0.55	230
Italy_University of Genoa	0.91	0.82	0.13	0.87	0.64	0.83	0.83	0.15	0.24	0.46	0.66	0.26	0.40	0.41	0.37	0.29	0.22	0.88	28
Czech Republic_Brno University of Technology	0.41	0.44	0.40	0.30	0.29	0.25	0.33	0.40	0.48	0.80	0.50	0.21	0.50	0.27	0.22	0.64	0.89	0.67	165
UK_University of Hertfordshire	0.23	0.13	0.43	0.38	0.59	0.64	0.29	0.47	0.74	0.84	0.91	0.30	0.71	0.43	0.39	0.19	0.09	0.81	66
North Macedonia_University of Sarajevo	0.24	0.27	0.00	0.17	0.27	0.42	0.14	0.00	0.13	0.16	0.96	0.08	0.33	0.12	0.08	0.06	0.06	0.40	306
UK_University of Greenwich	0.22	0.12	0.60	0.31	0.79	0.46	0.29	0.51	0.84	0.94	0.79	0.66	0.82	0.40	0.35	0.26	0.17	0.75	101
USA_California State University, Long Beach	0.13	0.08	0.13	0.18	0.76	0.32	0.17	0.10	0.70	0.35	0.27	0.21	0.38	0.49	0.43	0.25	0.13	0.45	279
USA_University of Arkansas	0.59	0.46	0.46	0.47	0.59	0.43	0.55	0.35	0.34	0.28	0.35	0.48	0.36	0.76	0.67	0.66	0.38	0.84	45
Russia_Reshetnev Siberian State University of Science and Technology	0.10	0.11	0.36	0.10	0.28	0.07	0.10	0.47	0.10	0.15	0.19	0.56	0.24	0.13	0.08	0.14	0.23	0.34	341
Italy_University of Palermo	0.41	0.42	0.33	0.63	0.96	0.55	0.61	0.31	0.07	0.06	0.40	0.32	0.20	0.29	0.23	0.11	0.07	0.61	194
UK_De Montfort University	0.23	0.14	0.19	0.23	0.00	0.57	0.21	0.20	0.71	0.86	0.52	0.56	0.67	0.32	0.27	0.09	0.04	0.63	183
Mexico_Metropolitan Autonomous University	0.20	0.29	0.24	0.18	0.31	0.27	0.16	0.35	0.44	0.04	0.25	0.60	0.33	0.29	0.22	0.49	0.87	0.60	199
Iran_University of Isfahan	0.58	0.62	0.49	0.41	0.13	0.16	0.54	0.10	0.09	0.09	0.11	0.08	0.08	0.35	0.31	0.10	0.05	0.40	308
UK_Leeds Beckett University	0.10	0.08	0.29	0.18	0.26	0.43	0.19	0.40	0.65	0.53	0.34	0.43	0.49	0.34	0.29	0.08	0.03	0.60	201
UK_University of Huddersfield	0.47	0.30	0.29	0.27	0.86	0.29	0.30	0.10	0.68	0.85	0.45	0.21	0.55	0.31	0.26	0.18	0.13	0.71	133
Kazakhstan_Suleyman Demirel University - Kazakhstan	0.00	0.00	0.00	0.61	0.00	0.17	0.92	0.00	0.56	0.24	0.06	0.08	0.22	0.02	0.02	0.04	0.16	0.27	373
USA_Kent State University	0.61	0.41	0.46	0.48	0.98	0.76	0.38	0.40	0.59	0.47	0.39	0.62	0.52	0.61	0.52	0.27	0.10	0.95	7
Russia_Saint-Petersburg state University of Architecture and Construction	0.06	0.07	0.09	0.07	0.06	0.23	0.06	0.10	0.08	0.37	0.10	0.08	0.14	0.16	0.11	0.11	0.11	0.17	404
China_Hunan University	0.51	0.51	0.36	0.59	0.30	0.85	0.54	0.40	0.33	0.14	0.16	0.38	0.24	0.45	0.39	0.68	0.75	0.71	134
Azerbaijan_Azerbaijan State University of Economics (UNEC)	0.07	0.06	0.00	0.03	0.13	0.17	0.02	0.00	0.06	0.07	0.15	0.08	0.07	0.10	0.07	0.01	0.00	0.12	413
UK_Glasgow Caledonian University	0.39	0.24	0.19	0.30	0.86	0.54	0.28	0.25	0.63	0.67	0.53	0.30	0.53	0.28	0.21	0.16	0.13	0.68	159
Spain_University of Seville	0.62	0.60	0.55	0.36	0.60	0.39	0.38	0.54	0.26	0.34	0.50	0.48	0.39	0.24	0.17	0.27	0.37	0.74	110
Russia_Siberian State University of Water Transport	0.08	0.09	0.00	0.10	0.08	0.08	0.10	0.00	0.12	0.17	0.19	0.08	0.13	0.14	0.10	0.16	0.26	0.21	396
Taiwan_Tatung University	0.21	0.16	0.00	0.31	0.73	0.14	0.36	0.00	0.12	0.15	0.04	0.08	0.08	0.26	0.19	0.31	0.35	0.36	328
Taiwan_Fu Jen Catholic University	0.28	0.13	0.36	0.27	0.37	0.21	0.29	0.35	0.42	0.48	0.09	0.43	0.35	0.33	0.27	0.60	0.80	0.63	182
Japan_Kindai University	0.09	0.07	0.13	0.37	0.77	0.34	0.31	0.20	0.46	0.12	0.07	0.21	0.20	0.83	0.72	0.25	0.06	0.49	262
USA_Western Michigan University	0.36	0.28	0.29	0.27	0.46	0.27	0.27	0.15	0.10	0.35	0.33	0.26	0.25	0.67	0.56	0.29	0.09	0.54	238
USA_North Dakota State University	0.71	0.52	0.36	0.47	0.98	0.37	0.54	0.20	0.38	0.33	0.28	0.43	0.35	0.75	0.66	0.77	0.66	0.91	20
Iraq_Middle Technical University	0.02	0.03	0.13	0.05	0.03	0.44	0.03	0.00	0.03	0.00	0.99	0.08	0.27	0.01	0.01	0.03	0.14	0.24	389
China_Guizhou University	0.05	0.05	0.00	0.20	0.09	0.30	0.19	0.00	0.14	0.04	0.16	0.08	0.09	0.27	0.19	0.29	0.37	0.27	375
China_Xiangtan University	0.16	0.11	0.09	0.32	0.31	0.48	0.29	0.10	0.33	0.10	0.08	0.08	0.13	0.24	0.16	0.48	0.69	0.41	303
Ireland_University of Limerick	0.46	0.39	0.36	0.50	0.46	0.48	0.51	0.40	0.89	0.71	0.63	0.38	0.66	0.35	0.28	0.54	0.71	0.91	19
Thailand_King Mongkuts University of Technology Thonburi | 0.30| 0.24| 0.40| 0.25| 0.36| 0.34| 0.26| 0.40| 0.38| 0.14| 0.51| 0.60| 0.40| 0.46| 0.38| 0.62| 0.71| 0.71| 131| |Iran_Shahid Beheshti University | 0.65| 0.73| 0.51| 0.10| 0.18| 0.26| 0.08| 0.40| 0.11| 0.11| 0.08| 0.24| 0.12| 0.46| 0.38| 0.50| 0.42| 0.58| 215| |Italy_Universita Cattolica del Sacro Cuore | 0.44| 0.32| 0.24| 0.59| 0.83| 0.62| 0.59| 0.31| 0.61| 0.39| 0.43| 0.56| 0.50| 0.40| 0.32| 0.26| 0.21| 0.79| 72| |Taiwan_National Taiwan Ocean University | 0.25| 0.22| 0.13| 0.46| 0.35| 0.16| 0.65| 0.10| 0.36| 0.40| 0.20| 0.21| 0.29| 0.52| 0.41| 0.74| 0.79| 0.54| 240| |Russia_Rostov State University of Economics | 0.11| 0.06| 0.00| 0.01| 0.08| 0.02| 0.02| 0.00| 0.07| 0.15| 0.00| 0.08| 0.06| 0.05| 0.03| 0.06| 0.09| 0.09| 417| |Thailand_King Mongkuts Institute of Technology Ladkrabang	0.33	0.24	0.13	0.17	0.89	0.10	0.19	0.54	0.40	0.07	0.24	0.48	0.29	0.39	0.31	0.80	0.91	0.71	132
Ireland_Dublin Institute of Technology	0.11	0.07	0.13	0.20	0.14	0.45	0.18	0.57	0.64	0.75	0.80	0.48	0.68	0.37	0.29	0.24	0.17	0.61	192
Taiwan_National Changhua University of Education	0.43	0.38	0.09	0.30	0.32	0.15	0.44	0.00	0.20	0.41	0.07	0.08	0.18	0.32	0.24	0.44	0.49	0.49	263
Republic of Korea_Chonbuk National University	0.63	0.44	0.24	0.60	0.61	0.31	0.73	0.25	0.31	0.22	0.36	0.28	0.29	0.56	0.43	0.70	0.73	0.85	36
Iraq_Imam Jaafar Al-Sadiq University | 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.10| 0.18| 0.03| 0.00| 0.18| 0.08| 0.07| 0.04| 0.08| 0.14| 0.07| 420| |UK_Aston University | 0.37| 0.28| 0.40| 0.49| 0.94| 0.60| 0.50| 0.47| 0.88| 0.82| 0.83| 0.60| 0.80| 0.48| 0.39| 0.33| 0.25| 0.99| 2| |Turkey_Hacettepe University | 0.68| 0.67| 0.79| 0.32| 0.87| 0.40| 0.30| 0.77| 0.24| 0.23| 0.20| 0.76| 0.36| 0.54| 0.42| 0.21| 0.15| 0.74| 115| |Iraq_Al-Esraa University College | 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.08| 0.00| 0.23| 0.15| 0.08| 0.07| 0.07| 418| |Mexico_Autonomous University of Mexico State | 0.11| 0.13| 0.24| 0.12| 0.67| 0.11| 0.12| 0.25| 0.18| 0.05| 0.35| 0.35| 0.22| 0.27| 0.18| 0.17| 0.19| 0.32| 348| |Iran_K. N. Toosi University of Technology | 0.81| 0.77| 0.33| 0.66| 0.05| 0.23| 0.94| 0.25| 0.36| 0.09| 0.08| 0.30| 0.19| 0.46| 0.36| 0.60| 0.55| 0.70| 140| |UK_London Metropolitan University | 0.28| 0.15| 0.33| 0.20| 0.97| 0.21| 0.22| 0.40| 0.77| 0.96| 0.64| 0.43| 0.71| 0.40| 0.30| 0.05| 0.02| 0.76| 93| |Taiwan_Ming Chuan University | 0.04| 0.03| 0.00| 0.16| 0.50| 0.12| 0.18| 0.10| 0.40| 0.55| 0.07| 0.18| 0.29| 0.25| 0.16| 0.23| 0.21| 0.37| 318| |Turkey_Istanbul Technical University | 0.33| 0.40| 0.81| 0.37| 0.12| 0.51| 0.30| 0.76| 0.28| 0.25| 0.42| 0.78| 0.43| 0.99| 0.97| 1.00| 0.99| 0.99| 3| |Thailand_Kasetsart University | 0.25| 0.17| 0.46| 0.19| 0.93| 0.19| 0.18| 0.51| 0.35| 0.06| 0.69| 0.48| 0.39| 0.46| 0.34| 0.53| 0.46| 0.73| 116| |North Macedonia_European University Skopje | 0.06| 0.06| 0.00| 0.00| 0.00| 0.02| 0.03| 0.00| 0.48| 0.92| 0.00| 0.08| 0.37| 0.16| 0.09| 0.03| 0.01| 0.20| 398| |Brazil_Pontificia Universidade Catolica do Rio Grande do Sul | 0.67| 0.47| 0.24| 0.22| 0.60| 0.28| 0.21| 0.10| 0.20| 0.04| 0.39| 0.18| 0.19| 0.39| 0.28| 0.41| 0.54| 0.60| 197| |Turkey_Istanbul Medipol University | 0.03| 0.05| 0.00| 0.16| 0.03| 0.10| 0.19| 0.00| 0.20| 0.13| 0.05| 0.08| 0.10| 0.51| 0.39| 0.24| 0.11| 0.20| 397| |Romania_University Politechica of Bucharest | 0.28| 0.07| 0.60| 0.38| 0.09| 0.23| 0.43| 0.51| 0.09| 0.18| 0.39| 0.24| 0.21| 0.23| 0.14| 0.51| 0.73| 0.52| 252| |USA_Northern Arizona University | 0.32| 0.19| 0.40| 0.31| 0.30| 0.83| 0.23| 0.35| 0.27| 0.26| 0.38| 0.48| 0.34| 0.51| 0.39| 0.30| 0.16| 0.62| 186| |Taiwan_Feng Chia University | 0.16| 0.10| 0.46| 0.25| 0.18| 0.15| 0.31| 0.51| 0.29| 0.67| 0.27| 0.43| 0.41| 0.35| 0.24| 0.55| 0.74| 0.62| 184| |Turkey_Bogazici University | 0.34| 0.30| 0.81| 0.60| 0.14| 0.90| 0.46| 0.74| 0.47| 0.19| 0.89| 0.80| 0.60| 0.44| 0.33| 0.44| 0.55| 0.93| 13| |India_Indian Institute of Technology (Indian School of Mines) | 0.96| 0.88| 0.09| 0.58| 0.59| 0.33| 0.84| 0.10| 0.00| 0.08| 0.03| 0.21| 0.06| 0.49| 0.36| 0.39| 0.28| 0.70| 142| |USA_State University of New York, Binghamton | 0.51| 0.34| 0.51| 0.43| 0.42| 0.47| 0.42| 0.40| 0.50| 0.62| 0.34| 0.48| 0.49| 0.71| 0.55| 0.47| 0.20| 0.82| 62| |Greece_University of Crete | 0.37| 0.32| 0.19| 0.80| 0.20| 0.77| 0.72| 0.31| 0.18| 0.24| 0.93| 0.35| 0.42| 0.19| 0.12| 0.46| 0.79| 0.84| 42| |Republic of Korea_Kyungpook National University | 0.68| 0.41| 0.43| 0.74| 0.33| 0.30| 0.89| 0.40| 0.43| 0.34| 0.29| 0.38| 0.35| 0.78| 0.61| 0.84| 0.70| 0.98| 4| |Kuwait_Kuwait University | 0.03| 0.03| 0.29| 0.21| 0.07| 0.25| 0.22| 0.15| 0.70| 0.63| 0.72| 0.21| 0.57| 0.98| 0.92| 0.23| 0.02| 0.64| 176| |Russia_Kozma Minin Nizhny Novgorod State Pedagogical University | 0.13| 0.10| 0.00| 0.04| 0.46| 0.02| 0.07| 0.00| 0.05| 0.21| 0.05| 0.08| 0.08| 0.07| 0.04| 0.14| 0.33| 0.20| 400| |Taiwan_National University of Kaohsiung | 0.00| 0.00| 0.00| 0.43| 0.00| 0.12| 0.56| 0.00| 0.37| 0.18| 0.15| 0.08| 0.18| 0.32| 0.20| 0.52| 0.59| 0.35| 336| |USA_Florida International University | 0.78| 0.37| 0.29| 0.51| 0.55| 0.68| 0.45| 0.25| 0.47| 0.41| 0.50| 0.53| 0.48| 0.77| 0.60| 0.50| 0.24| 0.85| 35| |Republic of Georgia_Ivane Javakhishvili Tbilisi State University | 0.23| 0.16| 0.33| 0.32| 0.06| 0.99| 0.19| 0.54| 0.60| 0.14| 0.98| 0.48| 0.56| 0.08| 0.05| 0.16| 0.73| 0.68| 160| |Iraq_Dijlah University College | 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.00| 0.22| 0.02| 0.00| 0.08| 0.06| 0.35| 0.23| 0.02| 0.01| 0.11| 414| |Iraq_University of Samarra | 0.05| 0.00| 0.00| 0.02| 0.04| 0.09| 0.02| 0.00| 0.00| 0.00| 0.00| 0.08| 0.00| 0.03| 0.03| 0.02| 0.04| 0.05| 427| |South Africa_University of Johannesburg | 0.32| 0.20| 0.40| 0.45| 0.48| 0.62| 0.42| 0.25| 0.80| 0.63| 0.86| 0.35| 0.67| 0.72| 0.55| 0.45| 0.26| 0.85| 39| |Japan_Shibaura Institute of Technology | 0.15| 0.09| 0.46| 0.23| 0.23| 0.11| 0.28| 0.54| 0.50| 0.68| 0.22| 0.48| 0.47| 0.88| 0.74| 0.28| 0.06| 0.62| 185| |Portugal_ISCTE – University Institute of Lisbon | 0.61| 0.58| 0.13| 0.26| 0.11| 0.29| 0.35| 0.20| 0.39| 0.57| 0.62| 0.35| 0.49| 0.20| 0.12| 0.43| 0.80| 0.60| 202| |Chile_Pontificial Catholic University of Valparaiso | 0.24| 0.20| 0.24| 0.24| 0.58| 0.20| 0.29| 0.20| 0.52| 0.07| 0.74| 0.28| 0.40| 0.34| 0.22| 0.33| 0.43| 0.60| 200| |USA_University of Texas at San Antonio | 0.31| 0.19| 0.46| 0.54| 0.65| 0.67| 0.47| 0.44| 0.16| 0.23| 0.52| 0.53| 0.36| 0.62| 0.44| 0.40| 0.23| 0.77| 91| |Iran_University of Tehran | 0.95| 0.93| 0.87| 0.54| 0.00| 0.35| 0.73| 0.85| 0.08| 0.12| 0.27| 0.78| 0.31| 0.12| 0.06| 0.21| 0.39| 0.84| 50| |Russia_Belgorod State Technological University | 0.00| 0.00| 0.19| 0.03| 0.00| 0.02| 0.04| 0.15| 0.30| 0.50| 0.02| 0.08| 0.21| 0.20| 0.12| 0.33| 0.81| 0.36| 331| |Taiwan_Tamkang University | 0.16| 0.10| 0.33| 0.24| 0.47| 0.16| 0.26| 0.31| 0.42| 0.40| 0.24| 0.30| 0.33| 0.26| 0.16| 0.31| 0.35| 0.51| 253| |Japan_Tokyo University of Science | 0.27| 0.17| 0.63| 0.62| 0.48| 0.31| 0.67| 0.64| 0.37| 0.12| 0.12| 0.69| 0.32| 0.48| 0.33| 0.36| 0.24| 0.72| 125| |Taiwan_National Yunlin University of Science and Technology | 0.27| 0.18| 0.09| 0.31| 0.14| 0.12| 0.43| 0.15| 0.20| 0.50| 0.03| 0.26| 0.24| 0.55| 0.38| 0.96| 0.98| 0.74| 106| |Egypt_Beni-Suef University | 0.16| 0.11| 0.00| 0.18| 0.11| 0.54| 0.15| 0.00| 0.37| 0.08| 0.92| 0.08| 0.36| 0.04| 0.03| 0.01| 0.01| 0.33| 343| |Italy_University of Ferrara | 0.60| 0.55| 0.33| 0.85| 0.86| 0.65| 0.82| 0.35| 0.06| 0.37| 0.72| 0.43| 0.39| 0.30| 0.17| 0.21| 0.21| 0.69| 150| |USA_University of Texas at Arlington | 0.50| 0.21| 0.33| 0.50| 0.83| 0.61| 0.44| 0.25| 0.29| 0.64| 0.62| 0.32| 0.47| 0.73| 0.54| 0.49| 0.23| 0.77| 84| |Jordan_Al-Ahliyya Amman University | 0.00| 0.00| 0.09| 0.10| 0.00| 0.09| 0.10| 0.00| 0.80| 0.99| 0.61| 0.18| 0.65| 0.22| 0.13| 0.00| 0.00| 0.40| 307| |Romania_Babes-Bolyai University | 0.27| 0.21| 0.58| 0.34| 0.10| 0.41| 0.35| 0.54| 0.68| 0.19| 0.66| 0.64| 0.55| 0.16| 0.08| 0.19| 0.32| 0.64| 178| |USA_Miami University | 0.24| 0.11| 0.46| 0.37| 0.54| 0.31| 0.43| 0.35| 0.22| 0.61| 0.23| 0.62| 0.42| 0.85| 0.66| 0.23| 0.05| 0.68| 156| |Jordan_University of Petra (UOP) | 0.00| 0.00| 0.00| 0.14| 0.00| 0.13| 0.12| 0.00| 0.62| 0.87| 0.76| 0.08| 0.59| 0.09| 0.04| 0.14| 0.30| 0.28| 370| |Iran_Kashan University | 0.50| 0.47| 0.00| 0.71| 0.05| 0.55| 0.81| 0.00| 0.18| 0.08| 0.03| 0.08| 0.08| 0.03| 0.02| 0.17| 0.77| 0.36| 327| |Australia_University of Southern Queensland | 0.41| 0.29| 0.09| 0.36| 0.35| 0.53| 0.37| 0.35| 0.77| 0.66| 0.74| 0.35| 0.64| 0.53| 0.34| 0.22| 0.10| 0.72| 130| |Taiwan_National Chiayi University | 0.12| 0.08| 0.00| 0.23| 0.24| 0.10| 0.28| 0.00| 0.11| 0.21| 0.06| 0.08| 0.10| 0.34| 0.20| 0.53| 0.67| 0.31| 356| |Thailand_University of the Thai Chamber of Commerce | 0.04| 0.04| 0.00| 0.05| 0.04| 0.06| 0.05| 0.00| 0.43| 0.20| 0.81| 0.08| 0.38| 0.16| 0.07| 0.15| 0.20| 0.28| 372| |Greece_Aristotle University of Thessaloniki | 0.42| 0.36| 0.58| 0.41| 0.16| 0.58| 0.36| 0.47| 0.08| 0.26| 0.66| 0.43| 0.35| 0.03| 0.02| 0.19| 0.99| 0.70| 138| |Iran_Alzahra University | 0.43| 0.36| 0.09| 0.32| 0.29| 0.33| 0.33| 0.00| 0.14| 0.06| 0.03| 0.08| 0.06| 0.36| 0.20| 0.08| 0.03| 0.34| 342| |Italy_University of Brescia | 0.26| 0.19| 0.19| 0.75| 0.00| 0.63| 0.78| 0.10| 0.35| 0.32| 0.52| 0.18| 0.34| 0.37| 0.20| 0.26| 0.22| 0.68| 155| |Iraq_University of Kirkuk | 0.06| 0.04| 0.00| 0.06| 0.26| 0.08| 0.04| 0.00| 0.40| 0.03| 0.97| 0.08| 0.37| 0.13| 0.05| 0.11| 0.32| 0.37| 320| |Egypt_Alexandria University | 0.35| 0.30| 0.40| 0.14| 0.21| 0.20| 0.14| 0.20| 0.15| 0.17| 0.90| 0.35| 0.39| 0.14| 0.06| 0.50| 0.96| 0.56| 224| |Greece_University of Patras | 0.40| 0.36| 0.24| 0.34| 0.22| 0.35| 0.32| 0.20| 0.09| 0.25| 0.58| 0.08| 0.24| 0.15| 0.06| 0.23| 0.78| 0.54| 234| |Italy_CaFoscari University of Venice	0.60	0.49	0.40	0.31	0.93	0.40	0.33	0.31	0.63	0.49	0.55	0.28	0.49	0.38	0.20	0.38	0.44	0.78	77
Italy_University of Turin	0.51	0.38	0.51	0.76	0.83	0.70	0.74	0.40	0.28	0.42	0.63	0.35	0.42	0.36	0.19	0.39	0.44	0.81	65
Iraq_Al-Farabi University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.29	0.15	0.17	0.11	0.07	421
Ireland_Maynooth University	0.44	0.23	0.43	0.68	0.40	0.88	0.44	0.10	0.91	0.56	0.84	0.30	0.66	0.62	0.40	0.59	0.49	0.95	8
Taiwan_I-Shou University	0.10	0.06	0.00	0.39	0.11	0.14	0.55	0.00	0.48	0.62	0.05	0.08	0.30	0.42	0.23	0.51	0.46	0.44	283
Turkey_Gebze Technical University	0.46	0.75	0.29	0.31	0.07	0.16	0.39	0.15	0.42	0.12	0.31	0.30	0.28	0.48	0.26	0.51	0.71	0.59	205
Turkey_Erciyes University	0.40	0.25	0.19	0.28	0.41	0.18	0.33	0.10	0.35	0.17	0.05	0.28	0.20	0.75	0.51	0.80	0.66	0.65	170
Australia_University of Canberra	0.46	0.19	0.29	0.73	0.63	0.88	0.73	0.31	0.63	0.89	0.44	0.43	0.60	0.64	0.40	0.32	0.16	0.82	59
Iran_Babol Noshirvani University of Technology	0.30	0.22	0.29	0.88	0.07	0.98	0.89	0.15	0.00	0.02	0.09	0.26	0.07	0.28	0.13	0.36	0.42	0.50	258
Taiwan_Asia University (Taiwan)	0.14	0.08	0.13	0.58	0.17	0.23	0.80	0.00	0.51	0.29	0.21	0.21	0.30	0.65	0.41	0.95	0.94	0.59	213
Latvia_Riga Technical University	0.54	0.45	0.29	0.20	0.20	0.44	0.20	0.25	0.65	0.53	0.78	0.48	0.62	0.35	0.17	0.58	0.86	0.67	162
Turkey_Gazi University	0.48	0.42	0.60	0.22	0.16	0.16	0.24	0.51	0.02	0.14	0.06	0.48	0.17	0.31	0.15	0.21	0.26	0.48	268
USA_San Diego State University	0.37	0.16	0.40	0.53	0.68	0.53	0.55	0.35	0.28	0.41	0.31	0.48	0.37	0.82	0.56	0.48	0.15	0.77	88
Canada_Universite du Quebec a Montreal	0.43	0.27	0.63	0.44	0.46	0.51	0.46	0.64	0.53	0.69	0.58	0.78	0.66	0.43	0.21	0.34	0.29	0.86	30
Italy_University of Bari	0.26	0.23	0.19	0.71	0.62	0.82	0.64	0.31	0.37	0.11	0.55	0.26	0.32	0.33	0.16	0.22	0.17	0.65	168
Taiwan_National Formosa University	0.03	0.03	0.00	0.26	0.06	0.12	0.36	0.00	0.12	0.08	0.02	0.08	0.06	0.39	0.18	0.49	0.49	0.34	338
India_Cochin University of Science and Technology	0.86	0.76	0.13	0.30	0.22	0.11	0.44	0.10	0.00	0.04	0.06	0.28	0.08	0.63	0.36	0.28	0.12	0.44	284
Iraq_Southern Technical University	0.00	0.00	0.00	0.04	0.00	0.11	0.02	0.00	0.00	0.00	0.99	0.08	0.26	0.04	0.02	0.02	0.03	0.12	412
Australia_Edith Cowan University	0.36	0.13	0.36	0.50	0.95	0.67	0.49	0.35	0.75	0.86	0.70	0.35	0.67	0.61	0.34	0.26	0.10	0.85	38
Iran_Allameh Tabataba’i University	0.82	0.73	0.09	0.14	0.17	0.51	0.13	0.00	0.16	0.08	0.41	0.08	0.17	0.12	0.04	0.14	0.27	0.42	292
Turkey_Middle East Technical University	0.62	0.54	0.92	0.32	0.31	0.37	0.30	0.89	0.41	0.31	0.42	0.89	0.51	0.62	0.34	0.43	0.68	0.94	10
Iran_Iran University of Science & Technology	0.88	0.50	0.57	0.75	0.41	0.29	0.97	0.47	0.00	0.05	0.07	0.24	0.07	0.70	0.41	0.87	0.80	0.70	137
Canada_Concordia University	0.44	0.26	0.43	0.42	0.23	0.39	0.53	0.44	0.84	0.88	0.53	0.60	0.72	0.50	0.24	0.37	0.28	0.78	82
Iraq_Madenat Al-elem University College	0.00	0.00	0.00	0.02	0.00	0.08	0.02	0.00	0.31	0.00	0.00	0.08	0.08	0.04	0.02	0.05	0.21	0.10	415
Taiwan_Chung Yuan Christian University	0.29	0.14	0.29	0.44	0.37	0.14	0.59	0.51	0.19	0.53	0.27	0.43	0.35	0.52	0.24	0.67	0.60	0.59	207
Iraq_Baghdad College Of Economic Sciences University	0.00	0.00	0.00	0.04	0.00	0.03	0.04	0.00	0.00	0.00	0.63	0.08	0.16	0.17	0.06	0.01	0.00	0.16	407
Thailand_Suranaree University of Technology	0.45	0.23	0.19	0.36	0.63	0.40	0.35	0.51	0.38	0.07	0.64	0.48	0.39	0.83	0.52	0.58	0.25	0.88	29
Thailand_Mahasarakham University	0.35	0.19	0.00	0.12	0.76	0.12	0.10	0.00	0.38	0.05	0.44	0.08	0.23	0.08	0.03	0.05	0.11	0.37	317
Iraq_University of Alkafeel	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.34	0.00	0.00	0.08	0.09	0.30	0.13	0.22	0.20	0.14	410
USA_University of Central Florida	0.65	0.26	0.55	0.46	0.54	0.58	0.47	0.64	0.39	0.20	0.43	0.72	0.43	0.77	0.42	0.55	0.28	0.86	34
Taiwan_Soochow University (Taiwan)	0.08	0.05	0.46	0.19	0.19	0.18	0.20	0.51	0.35	0.25	0.10	0.43	0.27	0.41	0.16	0.26	0.16	0.42	294
Egypt_Cairo University	0.46	0.22	0.73	0.24	0.32	0.38	0.22	0.66	0.21	0.14	0.64	0.74	0.43	0.19	0.06	0.08	0.07	0.59	212
Vietnam_Can Tho University	0.07	0.04	0.00	0.13	0.36	0.27	0.11	0.00	0.00	0.03	0.98	0.08	0.26	0.05	0.02	0.14	0.50	0.31	357
Egypt_Kafrelsheikh University	0.22	0.13	0.00	0.15	0.07	0.62	0.13	0.00	0.22	0.09	0.97	0.08	0.33	0.10	0.03	0.11	0.27	0.36	330
Iraq_Al-Kunooze University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.21	0.00	0.00	0.08	0.05	0.01	0.01	0.02	0.06	0.06	423
France_Universite de Paris-Nord - Paris 13	0.43	0.30	0.19	0.52	0.13	0.44	0.62	0.00	0.72	0.45	0.51	0.24	0.48	0.17	0.04	0.49	0.86	0.79	76
Taiwan_Chaoyang University of Technology	0.11	0.05	0.46	0.18	0.40	0.09	0.22	0.51	0.23	0.39	0.05	0.43	0.27	0.44	0.15	0.36	0.24	0.49	264
Turkey_Ataturk University	0.53	0.27	0.00	0.27	0.66	0.18	0.26	0.00	0.26	0.14	0.04	0.08	0.11	0.32	0.11	0.43	0.70	0.44	282
Australia_Australian Catholic University	0.24	0.10	0.29	0.49	0.79	0.65	0.59	0.40	0.87	0.56	0.55	0.38	0.60	0.72	0.29	0.26	0.08	0.84	44
Greece_Athens University of Economics and Business	0.45	0.25	0.19	0.29	0.51	0.28	0.38	0.20	0.12	0.26	0.82	0.21	0.35	0.20	0.05	0.60	0.89	0.54	233
Israel_Interdisciplinary Center Herzliya (IDC Herzliya)	0.00	0.00	0.00	0.20	0.00	0.34	0.21	0.00	0.09	0.83	0.60	0.08	0.40	0.65	0.21	0.13	0.13	0.23	390
Italy_University of Rome III	0.58	0.35	0.40	0.54	0.37	0.72	0.48	0.35	0.48	0.26	0.76	0.28	0.44	0.47	0.13	0.30	0.31	0.73	119
Mexico_Universidad de Guadalajara	0.24	0.12	0.24	0.17	0.29	0.12	0.15	0.25	0.21	0.04	0.41	0.28	0.22	0.71	0.22	0.27	0.15	0.43	289
Turkey_Istanbul University	0.80	0.47	0.72	0.32	0.35	0.19	0.39	0.70	0.41	0.32	0.14	0.70	0.39	0.46	0.09	0.83	0.96	0.81	67
South Africa_University of South Africa	0.47	0.07	0.36	0.18	1.00	0.26	0.24	0.25	0.45	0.36	0.43	0.35	0.40	0.78	0.09	0.13	0.02	0.69	147

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a strong positive relationship between the two ranking.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.8650477

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 1788266, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.8650477

The Impact of Changing the Threshold

The change of the threshold shows its impacts on leagues. The thresholds are 1-0.75 (specifies Q3 leagues) and 1-0.9 (specifies D9 leagues).

The Q3 League C

Calculating the Lower Q3 League C Bicluster

The next step is to identify the lower Q3 league bicluster.

rmtx<-1-mtx
rres <- iBBiG(binaryMatrix=binarize(rmtx,threshold = 0.75),nModules = 1,alpha=0.33,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(rres)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 1410.066 and 
##   192 Rows and  15 columns

The results of the iBBiG algorithm can be seen above. The algorithm found one bicluster in which there are 192 rows (HEIs) and 15 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant or not.

Calculating F-tests of the Lower Q3 League C Bicluster

In Table 14 the results of the row and column effects (F-tests) can be read. Both the row and column effects are significant, so the lower Q3 league bicluster is significant.

Obs.FStat <- NULL
for (i in c(1:rres@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=rres,number=i)
}
kable(Obs.FStat,caption = "**Table 14** The results of row and column effects for the lower (Q3) league")

Table 14 The results of row and column effects for the lower (Q3) league

Fstat PValue Row Effect 3.471552 0.0000000 Column Effect 12.651988 0.0000000 Tukey test 1.775095 0.1828664

To see the differences between those HEIs that are included in the lower league and those that are not in the lower league, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 23). (The horizontal axis of Fig. 23 shows the HEIs, the vertical axis shows the mentioned parameters on normalized (0-1) data of indicators.) On Fig. 23 the red line indicates those HEIs that are included in the lower league, while the black line shows the remaining HEIs. The HEIs in the lower league have higher means and medians, and have lower variances.

exploreBic(dset=mtx,bres=rres,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 23 Mean, median, variance and MAD for the lower Q3 league HEIs

One can do the same for the columns (indicators). Fig. 24 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. (The horizontal axis of Fig. 24 shows the indicators, the vertical axis shows the mentioned parameters on normalized (0-1) data of HEIs.) The red line indicates those indicators that are in the lower league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=rres,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 24 Mean, median, variance and MAD for the lower Q3 league indicators

Heat Maps of the Lower Q3 League C

Fig. 25 depicts the heat map of the lower Q3 league. The lower league contains 192 HEIs and 15 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=rres,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 25 Heat map of the lower league

Fig. 26 shows the heat map of the results of iBBiG on normalized data. The lower league can be seen in the upper left corner of Fig. 26 which is enlarged on Fig. 25.

drawHeatmap(x=mtx,bicResult=rres,local=FALSE,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 26 Heat map of the output after applying iBBiG on normalized data

Checking the Stability of the Lower Q3 League C Bicluster

The next step is to check the stability of the lower league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=rres,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 1.1346220 1.7246512
##   [2,] 1.2284824 1.4969680
##   [3,] 1.0644934 0.2755288
##   [4,] 1.0392018 0.9032583
##   [5,] 0.9979667 1.4838121
##   [6,] 1.2174318 0.6883583
##   [7,] 0.9611290 0.9689052
##   [8,] 0.8418212 1.0646394
##   [9,] 1.0854233 0.9649596
##  [10,] 1.0241670 1.3591502
##  [11,] 0.9608506 1.1011497
##  [12,] 0.9426786 0.7167657
##  [13,] 0.9142851 1.2235522
##  [14,] 1.0725213 0.9621779
##  [15,] 0.9901920 0.5857285
##  [16,] 1.0568263 1.5619685
##  [17,] 0.9987146 0.7977896
##  [18,] 1.2345716 1.0722392
##  [19,] 1.0773565 0.8150942
##  [20,] 1.0339060 1.1172004
##  [21,] 1.0010921 1.6869969
##  [22,] 1.0478400 0.8884631
##  [23,] 1.0472153 0.7869641
##  [24,] 0.8209609 0.8098253
##  [25,] 1.1443821 1.0838170
##  [26,] 0.9124266 1.6929268
##  [27,] 1.1387344 1.2746495
##  [28,] 1.1125787 0.5226662
##  [29,] 0.7793693 0.6663301
##  [30,] 1.0799942 1.7534225
##  [31,] 1.0308469 1.6175309
##  [32,] 1.1225386 0.5987368
##  [33,] 0.8644892 1.2257647
##  [34,] 0.9407072 1.5316862
##  [35,] 0.9040662 1.1524228
##  [36,] 1.0067799 0.7570320
##  [37,] 1.1096299 1.7919178
##  [38,] 1.2970232 0.4376241
##  [39,] 0.8818019 0.5974030
##  [40,] 1.0024075 1.2464509
##  [41,] 1.1161974 0.5364871
##  [42,] 1.0628210 0.4303755
##  [43,] 1.1142671 0.7500426
##  [44,] 0.9584590 0.8190445
##  [45,] 0.9321269 0.7699721
##  [46,] 1.0458544 1.0865598
##  [47,] 1.1279298 1.1315625
##  [48,] 0.9966410 0.7543168
##  [49,] 0.8682687 0.6728694
##  [50,] 1.0102708 0.9363063
##  [51,] 0.9350361 0.9609271
##  [52,] 1.0471460 0.7002710
##  [53,] 1.0953821 0.8409138
##  [54,] 0.9022104 0.7118255
##  [55,] 1.1191610 1.6906617
##  [56,] 1.0743818 1.1202011
##  [57,] 0.9996124 0.8086031
##  [58,] 1.0047539 1.8175768
##  [59,] 1.0827484 0.4336473
##  [60,] 1.0445418 1.6153020
##  [61,] 0.9003234 0.9807364
##  [62,] 0.8732914 0.7705991
##  [63,] 1.0202136 1.0167442
##  [64,] 0.9808242 0.6747080
##  [65,] 0.9717269 0.5263464
##  [66,] 0.8641766 1.5298948
##  [67,] 1.0998759 0.6972522
##  [68,] 1.1354529 1.7436053
##  [69,] 0.8012027 0.8427738
##  [70,] 0.9624299 0.8523900
##  [71,] 1.1727565 0.9316863
##  [72,] 1.1463766 1.2365725
##  [73,] 1.1618158 1.2011857
##  [74,] 0.9905490 1.0767618
##  [75,] 0.9976769 0.8855706
##  [76,] 1.0517807 0.8715837
##  [77,] 0.8550268 0.8606220
##  [78,] 0.9945083 1.5983845
##  [79,] 1.0194398 1.2618819
##  [80,] 1.1419173 1.3133917
##  [81,] 1.0826511 1.0814980
##  [82,] 0.8401250 0.5850069
##  [83,] 1.1591625 1.1246819
##  [84,] 0.8748535 1.8648701
##  [85,] 1.0305646 0.7157651
##  [86,] 1.1176092 0.9948202
##  [87,] 0.9019070 1.0922713
##  [88,] 0.9069623 1.1649626
##  [89,] 0.8835643 0.8727355
##  [90,] 0.9082215 0.4136790
##  [91,] 0.9916412 1.8529855
##  [92,] 1.1705626 0.7379912
##  [93,] 1.1009984 1.2840614
##  [94,] 1.0136647 0.8361407
##  [95,] 0.9527624 1.0552024
##  [96,] 0.9520972 0.8953922
##  [97,] 1.0632558 1.1903098
##  [98,] 0.9844552 0.7921992
##  [99,] 1.0384362 0.9064696
## [100,] 0.9197432 1.1144635
## 
## $observedFstatRow
## [1] 3.471552
## 
## $observedFstatCol
## [1] 12.65199
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

Since the bootstrapPvalueCol and the bootstrapPvalueRow are lower than 0.01, the bicluster is stable both for rows and columns.

Calculating Partial Rankings for Lower Q3 League C

The next step is to calculate partial rankings based on the indicators and HEIs in the lower league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR’s indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 15 shows the result of partial ranking in the case of the lower league.

C<-biclust::bicluster(mtx,rres,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 15** Q3 League C by iBBiG",digits = 2)

Table 15 Q3 League C by iBBiG

	T3	T4	T5	R1	R2	R3	R4	R5	I1	I2	I4	F1	F2	F4	F5	Overall_Score	Rank
Belarus_National Institute of Higher Education	0.12	0.00	0.19	0.00	0.05	0.00	0.00	0.15	0.00	0.00	0.26	0.94	1.00	0.98	0.75	0.56	31
Iraq_Al-Karkh University of Science	0.00	0.00	0.00	0.03	0.00	0.03	0.03	0.00	0.24	0.00	0.08	0.01	0.01	0.20	1.00	0.32	112
Iraq_University of Information Technology and Communications	0.00	0.00	0.00	0.01	0.00	0.02	0.02	0.00	0.00	0.00	0.08	0.11	0.86	0.13	0.21	0.12	173
Iraq_Al-Qasim green university Iraq	0.00	0.00	0.00	0.06	0.00	0.14	0.07	0.00	0.00	0.00	0.08	0.09	0.63	0.09	0.12	0.14	166
Russia_European University at St. Petersburg	0.00	0.00	0.33	0.10	0.00	0.17	0.17	0.31	0.55	0.77	0.08	0.25	0.88	0.24	0.36	0.49	51
Russia_Mechnikov St Petersburg State Medical Academy	0.03	0.03	0.00	0.11	0.73	0.49	0.06	0.00	0.03	0.40	0.08	0.62	0.96	0.06	0.01	0.39	83
Kazakhstan_Shakarim University	0.04	0.04	0.00	0.02	0.97	0.02	0.02	0.00	0.00	0.00	0.08	0.02	0.10	0.03	0.39	0.14	167
Iraq_Hawler Medical University	0.03	0.05	0.00	0.00	0.06	0.00	0.00	0.00	0.19	0.11	0.08	0.44	0.87	0.29	0.18	0.34	104
Russia_Ufa State Aviation Technical University	0.04	0.06	0.24	0.09	0.04	0.24	0.08	0.31	0.03	0.09	0.43	0.03	0.10	0.01	0.01	0.22	146
Kazakhstan_L.N. Gumilyov Eurasian National University	0.08	0.15	0.43	0.11	0.23	0.20	0.08	0.25	0.60	0.17	0.24	0.04	0.13	0.07	0.39	0.44	66
Japan_Tottori University	0.23	0.38	0.09	0.33	0.79	0.16	0.40	0.10	0.31	0.11	0.21	0.25	0.58	0.18	0.15	0.62	15
Canada_University of Quebec at Chicoutimi	0.00	0.00	0.19	0.24	0.00	0.37	0.22	0.25	0.00	0.84	0.38	0.43	0.78	0.67	0.66	0.58	24
Russia_Tver State Technical University	0.19	0.28	0.09	0.10	0.14	0.06	0.10	0.00	0.00	0.67	0.08	0.06	0.15	0.11	0.27	0.35	98
Russia_Bashkirian State Medical University	0.06	0.98	0.00	0.07	0.08	0.10	0.07	0.00	0.07	0.44	0.08	0.13	0.31	0.06	0.05	0.29	126
Russia_Kursk State Medical University	0.35	0.79	0.00	0.06	0.55	0.11	0.05	0.00	0.04	0.96	0.08	0.06	0.14	0.06	0.09	0.44	68
Ukraine_National University of Ostroh Academy	0.20	0.37	0.13	0.01	0.14	0.09	0.02	0.51	0.57	0.06	0.43	0.03	0.05	0.02	0.03	0.37	90
Ukraine_National Technical University Kharkiv Polytechnic Institute	0.12	0.20	0.19	0.08	0.34	0.08	0.08	0.35	0.08	0.47	0.21	0.02	0.05	0.04	0.21	0.37	88
Russia_Siberian State Medical University	0.08	0.14	0.00	0.12	0.22	0.15	0.12	0.00	0.10	0.76	0.08	0.14	0.31	0.10	0.11	0.34	105
Russia_Gubkin Russian State University of Oil and Gas	0.07	0.15	0.13	0.11	0.07	0.05	0.13	0.54	0.06	0.36	0.53	0.24	0.51	0.41	0.59	0.54	33
Ukraine_National Taras Shevchenko University of Kyiv	0.26	0.45	0.63	0.18	0.78	0.12	0.17	0.57	0.10	0.17	0.43	0.05	0.12	0.07	0.19	0.62	14
Argentina_Austral University (Argentina)	0.05	0.14	0.19	0.14	0.73	0.31	0.11	0.35	0.32	0.38	0.48	0.14	0.29	0.05	0.04	0.38	85
Russia_Perm National Research Polytechnic University	0.13	0.20	0.09	0.09	0.13	0.03	0.13	0.10	0.06	0.39	0.08	0.15	0.30	0.59	0.94	0.36	94
Russia_Kazan National Research Technical University named after A.N. Tupolev	0.17	0.27	0.19	0.09	0.15	0.06	0.12	0.10	0.27	0.48	0.18	0.20	0.42	0.47	0.74	0.46	59
China_Jiangsu University	0.10	0.20	0.00	0.28	0.45	0.51	0.24	0.00	0.78	0.23	0.08	0.15	0.26	0.34	0.86	0.36	96
India_Jamia Millia Islamia	0.67	0.79	0.13	0.17	0.35	0.31	0.14	0.10	0.25	0.15	0.18	0.20	0.40	0.09	0.23	0.56	29
Pakistan_Institute of Space Technology	0.00	0.00	0.00	0.03	0.00	0.00	0.01	0.00	0.00	0.00	0.08	0.18	0.35	0.13	0.17	0.15	162
Tunisia_University of Monastir	0.35	0.52	0.29	0.20	0.10	0.14	0.23	0.10	0.05	0.11	0.43	0.01	0.01	0.02	0.11	0.24	141
Russia_Magnitogorsk State Technical University	0.04	0.05	0.00	0.05	0.04	0.03	0.06	0.00	0.00	0.19	0.08	0.06	0.12	0.16	0.47	0.23	144
Iraq_University of AL-Qadisiyah	0.14	0.15	0.00	0.08	0.11	0.51	0.05	0.15	0.16	0.03	0.08	0.01	0.01	0.03	0.46	0.26	130
Tunisia_Universite de Tunis El Manar	0.62	0.84	0.19	0.22	0.08	0.16	0.24	0.20	0.32	0.10	0.53	0.02	0.04	0.19	0.88	0.51	44
Russia_The New Economic School	0.00	0.00	0.13	0.22	0.00	0.20	0.29	0.10	0.89	0.10	0.08	0.73	0.85	0.34	0.16	0.51	43
Ukraine_Kharkiv National University of Radio Electronics	0.14	0.17	0.13	0.07	0.13	0.21	0.05	0.31	0.04	0.47	0.08	0.03	0.05	0.04	0.10	0.30	124
Spain_University of Valladolid	0.17	0.99	0.09	0.26	0.12	0.25	0.24	0.15	0.29	0.28	0.48	0.15	0.24	0.12	0.19	0.43	69
Russia_Altai State University	0.12	0.29	0.09	0.12	0.60	0.18	0.12	0.10	0.36	0.61	0.08	0.08	0.14	0.19	0.47	0.57	27
Russia_Far Eastern Federal University	0.16	0.25	0.13	0.17	0.11	0.11	0.20	0.31	0.62	0.74	0.21	0.37	0.60	0.30	0.24	0.60	21
Ukraine_Poltava National Technical Yuri Kondratyuk University	0.00	0.00	0.09	0.03	0.00	0.04	0.04	0.10	0.00	0.30	0.08	0.00	0.00	0.00	0.00	0.06	186
Iraq_University of Baghdad	0.29	0.44	0.33	0.07	0.65	0.20	0.05	0.31	0.17	0.03	0.18	0.13	0.19	0.05	0.08	0.48	53
Romania_Grigore T. Popa University of Medicine and Pharmacy	0.14	0.21	0.13	0.31	0.23	0.20	0.38	0.00	0.03	0.85	0.08	0.11	0.18	0.04	0.04	0.37	91
Russia_Perm State University	0.07	0.09	0.19	0.12	0.16	0.04	0.15	0.15	0.12	0.10	0.08	0.08	0.14	0.16	0.40	0.23	142
Iraq_Mustansiriyah University	0.16	0.22	0.13	0.05	0.70	0.17	0.03	0.15	0.05	0.02	0.08	0.12	0.18	0.01	0.01	0.25	134
Russia_Kazan National Research Technological University	0.15	0.29	0.09	0.11	0.38	0.05	0.13	0.00	0.08	0.51	0.08	0.12	0.18	0.31	0.66	0.36	92
Russia_Russian New University	0.12	0.24	0.09	0.03	0.15	0.04	0.03	0.10	0.16	0.48	0.08	0.06	0.10	0.09	0.22	0.19	152
Russia_Moscow Pedagogical State University	0.12	0.18	0.24	0.09	0.26	0.07	0.09	0.10	0.11	0.49	0.21	0.10	0.16	0.08	0.11	0.37	89
Tunisia_Universite de Carthage	0.33	0.57	0.00	0.16	0.83	0.17	0.17	0.10	0.13	0.05	0.08	0.01	0.01	0.02	0.09	0.35	97
Russia_Voronezh State University	0.21	0.27	0.19	0.13	0.19	0.07	0.16	0.31	0.23	0.48	0.43	0.07	0.12	0.12	0.31	0.39	79
Republic of Korea_Kookmin University	0.18	0.22	0.09	0.22	0.21	0.26	0.18	0.15	0.38	0.47	0.21	0.17	0.28	0.32	0.59	0.64	12
Russia_Russian State University for the Humanities	0.11	0.08	0.49	0.05	0.05	0.06	0.09	0.47	0.24	0.31	0.48	0.00	0.00	0.01	0.10	0.34	101
Ukraine_Kyiv National Economic University	0.11	0.15	0.36	0.00	0.20	0.00	0.01	0.54	0.04	0.05	0.43	0.02	0.03	0.01	0.02	0.23	143
Russia_Saratov State University	0.20	0.33	0.24	0.21	0.22	0.15	0.22	0.25	0.08	0.31	0.18	0.16	0.23	0.44	0.82	0.60	20
Russia_Northeast Federal University	0.69	0.81	0.09	0.13	0.66	0.28	0.11	0.00	0.55	0.22	0.08	0.20	0.32	0.20	0.22	0.73	2
Colombia_Universidad Pontificia Bolivariana de Medellin-Colombia	0.05	0.12	0.24	0.13	0.15	0.30	0.10	0.60	0.16	0.09	0.60	0.25	0.41	0.20	0.18	0.40	76
Russia_National Research University of Electronic Technology (MIET)	0.19	0.24	0.29	0.12	0.12	0.04	0.17	0.31	0.23	0.24	0.56	0.41	0.60	0.79	0.91	0.70	7
Russia_Novosibirsk State Technical University	0.10	0.14	0.43	0.15	0.07	0.10	0.16	0.47	0.17	0.75	0.43	0.10	0.14	0.21	0.49	0.51	41
Russia_Ryazan State Medical University	0.13	0.31	0.09	0.03	0.95	0.04	0.04	0.00	0.13	0.65	0.08	0.09	0.13	0.07	0.09	0.25	137
Russia_Moscow State University of Design and Technology (MSUDT)	0.09	0.11	0.09	0.04	0.26	0.01	0.10	0.00	0.13	0.40	0.21	0.07	0.11	0.07	0.10	0.20	149
Russia_Financial University under the Government of the Russian Federation	0.15	0.19	0.90	0.05	0.09	0.18	0.09	0.91	0.08	0.40	0.93	0.23	0.36	0.15	0.13	0.70	6
Russia_Mordovia State University	0.12	0.15	0.29	0.09	0.13	0.08	0.09	0.51	0.09	0.52	0.43	0.10	0.14	0.14	0.28	0.35	99
Russia_Bashkir State University	0.19	0.26	0.13	0.15	0.42	0.08	0.16	0.10	0.03	0.20	0.08	0.07	0.11	0.16	0.43	0.40	77
Russia_Volgograd State University	0.18	0.20	0.00	0.10	0.39	0.03	0.12	0.00	0.14	0.19	0.08	0.07	0.11	0.09	0.19	0.28	128
Russia_Irkutsk State University	0.08	0.09	0.24	0.13	0.09	0.15	0.13	0.15	0.15	0.24	0.08	0.06	0.10	0.10	0.27	0.26	133
Russia_Plekhanov Russian University of Economics	0.32	0.26	0.19	0.06	0.47	0.07	0.07	0.25	0.44	0.43	0.26	0.24	0.35	0.11	0.08	0.52	36
Iraq_Jabir Ibn Hayyan Medical University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.99	0.98	0.99	0.62	0.45	65
Poland_Lodz University of Technology	0.13	0.20	0.13	0.26	0.17	0.16	0.32	0.15	0.15	0.22	0.08	0.19	0.27	0.25	0.34	0.33	111
Russia_Orel State University	0.18	0.24	0.70	0.03	0.41	0.04	0.03	0.74	0.00	0.20	0.70	0.05	0.06	0.20	0.71	0.61	19
Russia_Don State Technical University	0.23	0.17	0.00	0.06	0.52	0.08	0.06	0.10	0.08	0.48	0.18	0.08	0.12	0.09	0.15	0.42	71
Russia_Northern (Arctic) Federal University (NArFU)	0.23	0.21	0.00	0.07	0.62	0.05	0.09	0.00	0.20	0.23	0.08	0.12	0.15	0.18	0.35	0.25	135
Azerbaijan_Baku State University	0.15	0.17	0.13	0.10	0.22	0.09	0.10	0.31	0.23	0.13	0.43	0.02	0.03	0.07	0.62	0.36	95
Thailand_Thammasat University	0.10	0.10	0.29	0.16	0.92	0.21	0.15	0.25	0.57	0.09	0.21	0.58	0.70	0.45	0.30	0.65	11
Iraq_Al-Noor University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.06	0.08	0.12	0.30	0.06	187
Kazakhstan_EA Buketov Karaganda State University	0.05	0.05	0.00	0.04	0.07	0.04	0.08	0.00	0.06	0.09	0.08	0.04	0.06	0.06	0.15	0.10	178
Russia_Samara University	0.09	0.12	0.19	0.16	0.09	0.07	0.16	0.25	0.05	0.14	0.35	0.10	0.13	0.21	0.53	0.34	103
Iraq_Al-Kitab University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.04	0.05	0.01	0.01	0.02	192
China_Hangzhou Dianzi University	0.00	0.00	0.13	0.29	0.00	0.52	0.27	0.15	0.29	0.04	0.30	0.19	0.24	0.30	0.45	0.45	62
Ukraine_Ostrogradskiy National University of Kremenchuk	0.04	0.04	0.49	0.02	0.03	0.02	0.03	0.54	0.21	0.03	0.48	0.03	0.04	0.03	0.06	0.33	110
Tunisia_Universite de la Manouba	0.24	0.35	0.00	0.17	0.04	0.16	0.17	0.00	0.14	0.07	0.08	0.05	0.07	0.03	0.03	0.15	163
Ukraine_South Ukrainian National Pedagogical University named after K.D. Ushynsky	0.33	0.32	0.13	0.05	0.09	0.07	0.06	0.25	0.18	0.28	0.24	0.03	0.03	0.04	0.12	0.33	109
Russia_Tyumen State University	0.13	0.16	0.09	0.13	0.12	0.23	0.14	0.10	0.26	0.33	0.08	0.18	0.22	0.32	0.52	0.48	56
Russia_Belgorod National Research University	0.30	0.25	0.19	0.15	0.15	0.32	0.14	0.15	0.21	0.72	0.08	0.14	0.16	0.35	0.73	0.56	30
India_Amity University	0.07	0.08	0.55	0.15	0.04	0.21	0.14	0.60	0.11	0.26	0.66	0.22	0.28	0.06	0.05	0.44	67
Iraq_University of Kufa	0.11	0.11	0.43	0.08	0.06	0.12	0.06	0.54	0.06	0.00	0.53	0.24	0.31	0.15	0.13	0.36	93
United Arab Emirates_American University of Sharjah	0.00	0.00	0.33	0.28	0.00	0.25	0.31	0.20	1.00	1.00	0.18	0.86	0.86	0.10	0.02	0.52	40
Taiwan_Tunghai University	0.06	0.06	0.00	0.19	0.15	0.14	0.19	0.00	0.41	0.36	0.08	0.15	0.17	0.22	0.37	0.26	131
Russia_Voronezh State Technical University	0.06	0.07	0.13	0.05	0.09	0.04	0.06	0.15	0.04	0.18	1.00	0.00	0.00	0.01	0.30	0.34	102
Russia_Immanuel Kant Baltic Federal University	0.22	0.27	0.19	0.14	0.09	0.11	0.15	0.20	0.17	0.27	0.08	0.15	0.17	0.15	0.26	0.31	120
Poland_University of Lodz	0.18	0.26	0.09	0.22	0.34	0.20	0.23	0.15	0.19	0.26	0.21	0.08	0.10	0.14	0.32	0.37	87
Iraq_University of Ahl al-Bayt	0.00	0.00	0.00	0.18	0.00	0.13	0.16	0.00	0.00	0.00	0.08	0.09	0.11	0.15	0.58	0.18	155
Russia_Samara State Technical University	0.11	0.14	0.13	0.11	0.15	0.06	0.12	0.15	0.05	0.12	0.24	0.13	0.14	0.26	0.58	0.26	132
China_Wuhan University of Science & Technology	0.09	0.09	0.09	0.20	0.27	0.34	0.20	0.10	0.25	0.07	0.21	0.14	0.15	0.28	0.55	0.45	63
Iraq_University of Babylon	0.19	0.16	0.09	0.08	0.20	0.37	0.05	0.10	0.03	0.02	0.08	0.16	0.17	0.08	0.17	0.24	138
Iraq_University of Tikrit	0.27	0.31	0.00	0.11	0.22	0.27	0.05	0.00	0.00	0.02	0.08	0.01	0.01	0.00	0.00	0.12	171
Puerto Rico_University of Puerto Rico	0.15	0.22	0.49	0.29	0.78	0.73	0.21	0.44	0.16	0.05	0.30	0.13	0.13	0.17	0.32	0.68	9
Iraq_University of Anbar	0.18	0.22	0.00	0.09	0.80	0.29	0.07	0.00	0.05	0.00	0.08	0.15	0.16	0.12	0.14	0.39	80
Iraq_Al-Maarif University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.07	0.08	0.10	0.22	0.08	183
Russia_Ufa State Petroleum Technological University (USPTU)	0.04	0.04	0.13	0.05	0.05	0.02	0.09	0.10	0.12	0.33	0.08	0.09	0.10	0.19	0.44	0.28	129
Russia_Southwest State University	0.29	0.29	0.00	0.08	0.39	0.09	0.08	0.10	0.10	0.28	0.08	0.06	0.07	0.25	0.74	0.50	48
Poland_Gdansk University of Technology	0.25	0.22	0.19	0.29	0.64	0.26	0.32	0.15	0.15	0.21	0.08	0.24	0.28	0.33	0.41	0.42	73
Russia_Tver State University	0.03	0.27	0.09	0.11	0.73	0.05	0.13	0.10	0.06	0.16	0.08	0.06	0.07	0.67	1.00	0.32	117
Russia_Tomsk State University of Control Systems and Radioelectronics (TUSUR University)	0.21	0.26	0.19	0.15	0.17	0.27	0.15	0.31	0.23	0.77	0.28	0.22	0.24	0.58	0.89	0.57	26
Russia_Volgograd State Technical University	0.09	0.10	0.00	0.09	0.16	0.02	0.11	0.00	0.03	0.36	0.08	0.10	0.11	0.25	0.58	0.17	157
Slovenia_University of Maribor	0.19	0.25	0.19	0.35	0.15	0.38	0.39	0.15	0.17	0.28	0.08	0.18	0.18	0.29	0.50	0.52	38
Iraq_University of Misan	0.00	0.00	0.00	0.06	0.00	0.09	0.05	0.00	0.00	0.00	0.08	0.17	0.18	0.05	0.03	0.11	176
Spain_ESIC Business and Marketing School	0.00	0.00	0.00	0.04	0.00	0.10	0.04	0.00	0.73	0.58	0.08	0.28	0.33	0.06	0.04	0.29	125
China_Yanshan University	0.20	0.23	0.00	0.24	0.58	0.33	0.24	0.00	0.24	0.06	0.08	0.23	0.24	0.45	0.76	0.59	22
Iraq_Iraq University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.57	0.00	0.08	0.08	0.09	0.04	0.05	0.16	159
Azerbaijan_Azerbaijan University of Architecture and Construction	0.17	0.15	0.00	0.02	0.73	0.03	0.03	0.10	0.24	0.43	0.08	0.05	0.06	0.03	0.03	0.34	107
Iraq_Uruk University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.16	0.00	0.08	0.01	0.01	0.02	0.30	0.12	175
Croatia_University of Rijeka	0.15	0.25	0.00	0.20	0.12	0.26	0.19	0.15	0.07	0.04	0.08	0.12	0.12	0.08	0.18	0.28	127
Thailand_Prince of Songkla University	0.16	0.13	0.40	0.21	0.81	0.20	0.20	0.47	0.33	0.12	0.43	0.42	0.45	0.18	0.08	0.51	46
Russia_Omsk State Technical University	0.17	0.19	0.09	0.07	0.75	0.06	0.09	0.00	0.04	0.74	0.18	0.07	0.07	0.16	0.41	0.56	28
Turkey_Ege University	0.19	0.30	0.00	0.26	0.30	0.16	0.23	0.00	0.22	0.18	0.08	0.40	0.43	0.28	0.33	0.50	47
Iraq_Islamic University in Najaf	0.03	0.03	0.00	0.02	0.04	0.00	0.01	0.00	0.00	0.00	0.08	0.21	0.20	0.04	0.02	0.09	181
Iraq_University of Diyala	0.14	0.14	0.00	0.06	0.42	0.30	0.04	0.00	0.00	0.00	0.08	0.02	0.02	0.03	0.17	0.19	153
China_China Medical University (Taiwan)	0.22	0.21	0.19	0.86	0.14	0.30	0.97	0.20	0.23	0.41	0.21	0.99	0.97	0.79	0.14	1.00	1
Turkey_Atilim University	0.08	0.09	0.13	0.19	0.38	0.32	0.21	0.10	0.29	0.25	0.28	0.21	0.19	0.16	0.18	0.30	123
Iraq_Al-Mustaqbal University College	0.00	0.00	0.00	0.08	0.00	0.23	0.05	0.00	0.22	0.00	0.08	0.16	0.15	0.20	0.30	0.21	148
Romania_George Emil Palade University of Medicine, Pharmacy, Science, and Technology of Targu Mures	0.17	0.21	0.00	0.17	0.27	0.12	0.16	0.00	0.11	0.35	0.08	0.14	0.13	0.04	0.06	0.25	136
Turkey_TOBB University of Economics and Technology	0.07	0.10	0.09	0.59	0.05	0.92	0.40	0.10	0.18	0.05	0.21	0.24	0.22	0.17	0.15	0.39	82
Taiwan_National Taipei University	0.15	0.12	0.29	0.19	0.28	0.22	0.23	0.31	0.17	0.22	0.48	0.23	0.21	0.25	0.29	0.53	35
Russia_Moscow State Institute of Radio Engineering, Electrical & Automation	0.07	0.07	0.74	0.14	0.05	0.06	0.17	0.73	0.07	0.16	0.70	0.21	0.18	0.44	0.73	0.73	3
Russia_South Ural State University	0.09	0.09	0.19	0.11	0.08	0.11	0.11	0.15	0.11	0.30	0.18	0.11	0.09	0.23	0.54	0.33	108
Iraq_University of Thi-Qar	0.09	0.10	0.00	0.10	0.12	0.24	0.06	0.00	0.00	0.00	0.08	0.12	0.10	0.12	0.33	0.24	140
Iraq_University College in Baghdad Iraq	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.10	0.09	0.07	0.12	0.07	185
Russia_Tomsk State University of Architecture and Building	0.07	0.08	0.00	0.08	0.89	0.04	0.11	0.15	0.10	0.65	0.08	0.00	0.00	0.00	0.38	0.46	60
Iraq_Al-Nisour University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.22	0.00	0.08	0.03	0.03	0.07	0.43	0.13	170
Egypt_Ain Shams University	0.30	0.30	0.43	0.15	0.06	0.37	0.11	0.10	0.43	0.16	0.60	0.10	0.08	0.05	0.10	0.49	50
Russia_Voronezh Institute of High Technologies	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.19	0.08	0.05	0.04	0.17	0.54	0.08	182
India_Vellore Institute of Technology	0.39	0.44	0.19	0.25	0.10	0.25	0.00	0.15	0.56	0.15	0.08	0.35	0.34	0.14	0.11	0.52	39
Romania_West University of Timisoara	0.29	0.17	0.19	0.40	0.17	0.87	0.26	0.15	0.09	0.24	0.08	0.11	0.08	0.10	0.14	0.51	45
Russia_Pacific National University	0.09	0.07	0.00	0.04	0.18	0.03	0.07	0.00	0.09	0.30	0.08	0.09	0.07	0.14	0.25	0.12	172
Pakistan_NED University of Engineering and Technology	0.04	0.03	0.00	0.15	0.08	0.23	0.12	0.00	0.04	0.03	0.08	0.09	0.07	0.10	0.17	0.15	165
Russia_North Caucasus Federal University	0.19	0.18	0.00	0.06	0.25	0.05	0.07	0.00	0.55	0.34	0.08	0.13	0.09	0.13	0.21	0.30	121
USA_Savannah College of Art and Design	0.00	0.00	0.00	0.02	0.00	0.01	0.08	0.00	0.52	0.85	0.08	0.68	0.61	0.82	0.70	0.52	37
Russia_Ulyanovsk State University	0.10	0.11	0.00	0.13	0.04	0.08	0.15	0.00	0.06	0.44	0.08	0.11	0.08	0.20	0.47	0.32	114
Russia_Novosibirsk State University of Economics and Management	0.06	0.05	0.00	0.02	0.08	0.06	0.04	0.00	0.05	0.17	0.08	0.00	0.00	0.00	0.08	0.10	180
North Macedonia_University of Sarajevo	0.24	0.27	0.00	0.17	0.27	0.42	0.14	0.00	0.13	0.16	0.08	0.12	0.08	0.06	0.06	0.24	139
USA_California State University, Long Beach	0.13	0.08	0.13	0.18	0.76	0.32	0.17	0.10	0.70	0.35	0.21	0.49	0.43	0.25	0.13	0.69	8
Russia_Reshetnev Siberian State University of Science and Technology	0.10	0.11	0.36	0.10	0.28	0.07	0.10	0.47	0.10	0.15	0.56	0.13	0.08	0.14	0.23	0.42	72
UK_De Montfort University	0.23	0.14	0.19	0.23	0.00	0.57	0.21	0.20	0.71	0.86	0.56	0.32	0.27	0.09	0.04	0.58	23
Iran_University of Isfahan	0.58	0.62	0.49	0.41	0.13	0.16	0.54	0.10	0.09	0.09	0.08	0.35	0.31	0.10	0.05	0.61	18
Kazakhstan_Suleyman Demirel University - Kazakhstan	0.00	0.00	0.00	0.61	0.00	0.17	0.92	0.00	0.56	0.24	0.08	0.02	0.02	0.04	0.16	0.39	81
Russia_Saint-Petersburg state University of Architecture and Construction	0.06	0.07	0.09	0.07	0.06	0.23	0.06	0.10	0.08	0.37	0.08	0.16	0.11	0.11	0.11	0.19	151
Azerbaijan_Azerbaijan State University of Economics (UNEC)	0.07	0.06	0.00	0.03	0.13	0.17	0.02	0.00	0.06	0.07	0.08	0.10	0.07	0.01	0.00	0.13	169
Russia_Siberian State University of Water Transport	0.08	0.09	0.00	0.10	0.08	0.08	0.10	0.00	0.12	0.17	0.08	0.14	0.10	0.16	0.26	0.18	154
Taiwan_Tatung University	0.21	0.16	0.00	0.31	0.73	0.14	0.36	0.00	0.12	0.15	0.08	0.26	0.19	0.31	0.35	0.32	116
Iraq_Middle Technical University	0.02	0.03	0.13	0.05	0.03	0.44	0.03	0.00	0.03	0.00	0.08	0.01	0.01	0.03	0.14	0.10	179
China_Guizhou University	0.05	0.05	0.00	0.20	0.09	0.30	0.19	0.00	0.14	0.04	0.08	0.27	0.19	0.29	0.37	0.32	115
China_Xiangtan University	0.16	0.11	0.09	0.32	0.31	0.48	0.29	0.10	0.33	0.10	0.08	0.24	0.16	0.48	0.69	0.43	70
Russia_Rostov State University of Economics	0.11	0.06	0.00	0.01	0.08	0.02	0.02	0.00	0.07	0.15	0.08	0.05	0.03	0.06	0.09	0.12	174
Ireland_Dublin Institute of Technology	0.11	0.07	0.13	0.20	0.14	0.45	0.18	0.57	0.64	0.75	0.48	0.37	0.29	0.24	0.17	0.72	4
Iraq_Imam Ja`afar Al-Sadiq University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.10	0.18	0.03	0.18	0.07	0.04	0.08	0.14	0.11	177
Iraq_Al-Esraa University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.23	0.15	0.08	0.07	0.07	184
Mexico_Autonomous University of Mexico State	0.11	0.13	0.24	0.12	0.67	0.11	0.12	0.25	0.18	0.05	0.35	0.27	0.18	0.17	0.19	0.46	61
Taiwan_Ming Chuan University	0.04	0.03	0.00	0.16	0.50	0.12	0.18	0.10	0.40	0.55	0.18	0.25	0.16	0.23	0.21	0.40	75
North Macedonia_European University Skopje	0.06	0.06	0.00	0.00	0.00	0.02	0.03	0.00	0.48	0.92	0.08	0.16	0.09	0.03	0.01	0.31	119
Turkey_Istanbul Medipol University	0.03	0.05	0.00	0.16	0.03	0.10	0.19	0.00	0.20	0.13	0.08	0.51	0.39	0.24	0.11	0.30	122
Romania_University Politechica of Bucharest	0.28	0.07	0.60	0.38	0.09	0.23	0.43	0.51	0.09	0.18	0.24	0.23	0.14	0.51	0.73	0.46	58
Kuwait_Kuwait University	0.03	0.03	0.29	0.21	0.07	0.25	0.22	0.15	0.70	0.63	0.21	0.98	0.92	0.23	0.02	0.72	5
Russia_Kozma Minin Nizhny Novgorod State Pedagogical University	0.13	0.10	0.00	0.04	0.46	0.02	0.07	0.00	0.05	0.21	0.08	0.07	0.04	0.14	0.33	0.17	158
Taiwan_National University of Kaohsiung	0.00	0.00	0.00	0.43	0.00	0.12	0.56	0.00	0.37	0.18	0.08	0.32	0.20	0.52	0.59	0.34	106
Republic of Georgia_Ivane Javakhishvili Tbilisi State University	0.23	0.16	0.33	0.32	0.06	0.99	0.19	0.54	0.60	0.14	0.48	0.08	0.05	0.16	0.73	0.63	13
Iraq_Dijlah University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.22	0.02	0.08	0.35	0.23	0.02	0.01	0.17	156
Iraq_University of Samarra	0.05	0.00	0.00	0.02	0.04	0.09	0.02	0.00	0.00	0.00	0.08	0.03	0.03	0.02	0.04	0.03	190
Chile_Pontificial Catholic University of Valparaiso	0.24	0.20	0.24	0.24	0.58	0.20	0.29	0.20	0.52	0.07	0.28	0.34	0.22	0.33	0.43	0.66	10
Russia_Belgorod State Technological University	0.00	0.00	0.19	0.03	0.00	0.02	0.04	0.15	0.30	0.50	0.08	0.20	0.12	0.33	0.81	0.51	42
Egypt_Beni-Suef University	0.16	0.11	0.00	0.18	0.11	0.54	0.15	0.00	0.37	0.08	0.08	0.04	0.03	0.01	0.01	0.21	147
Jordan_Al-Ahliyya Amman University	0.00	0.00	0.09	0.10	0.00	0.09	0.10	0.00	0.80	0.99	0.18	0.22	0.13	0.00	0.00	0.47	57
Jordan_University of Petra (UOP)	0.00	0.00	0.00	0.14	0.00	0.13	0.12	0.00	0.62	0.87	0.08	0.09	0.04	0.14	0.30	0.48	55
Iran_Kashan University	0.50	0.47	0.00	0.71	0.05	0.55	0.81	0.00	0.18	0.08	0.08	0.03	0.02	0.17	0.77	0.54	34
Taiwan_National Chiayi University	0.12	0.08	0.00	0.23	0.24	0.10	0.28	0.00	0.11	0.21	0.08	0.34	0.20	0.53	0.67	0.49	52
Thailand_University of the Thai Chamber of Commerce	0.04	0.04	0.00	0.05	0.04	0.06	0.05	0.00	0.43	0.20	0.08	0.16	0.07	0.15	0.20	0.22	145
Iran_Alzahra University	0.43	0.36	0.09	0.32	0.29	0.33	0.33	0.00	0.14	0.06	0.08	0.36	0.20	0.08	0.03	0.45	64
Iraq_University of Kirkuk	0.06	0.04	0.00	0.06	0.26	0.08	0.04	0.00	0.40	0.03	0.08	0.13	0.05	0.11	0.32	0.16	161
Egypt_Alexandria University	0.35	0.30	0.40	0.14	0.21	0.20	0.14	0.20	0.15	0.17	0.35	0.14	0.06	0.50	0.96	0.54	32
Greece_University of Patras	0.40	0.36	0.24	0.34	0.22	0.35	0.32	0.20	0.09	0.25	0.08	0.15	0.06	0.23	0.78	0.41	74
Iraq_Al-Farabi University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.29	0.15	0.17	0.11	0.13	168
Taiwan_I-Shou University	0.10	0.06	0.00	0.39	0.11	0.14	0.55	0.00	0.48	0.62	0.08	0.42	0.23	0.51	0.46	0.62	16
Turkey_Gazi University	0.48	0.42	0.60	0.22	0.16	0.16	0.24	0.51	0.02	0.14	0.48	0.31	0.15	0.21	0.26	0.48	54
Taiwan_National Formosa University	0.03	0.03	0.00	0.26	0.06	0.12	0.36	0.00	0.12	0.08	0.08	0.39	0.18	0.49	0.49	0.39	78
Iraq_Southern Technical University	0.00	0.00	0.00	0.04	0.00	0.11	0.02	0.00	0.00	0.00	0.08	0.04	0.02	0.02	0.03	0.03	189
Iran_Allameh Tabataba’i University	0.82	0.73	0.09	0.14	0.17	0.51	0.13	0.00	0.16	0.08	0.08	0.12	0.04	0.14	0.27	0.32	113
Iraq_Madenat Al-elem University College	0.00	0.00	0.00	0.02	0.00	0.08	0.02	0.00	0.31	0.00	0.08	0.04	0.02	0.05	0.21	0.16	160
Iraq_Baghdad College Of Economic Sciences University	0.00	0.00	0.00	0.04	0.00	0.03	0.04	0.00	0.00	0.00	0.08	0.17	0.06	0.01	0.00	0.05	188
Thailand_Mahasarakham University	0.35	0.19	0.00	0.12	0.76	0.12	0.10	0.00	0.38	0.05	0.08	0.08	0.03	0.05	0.11	0.35	100
Iraq_University of Alkafeel	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.34	0.00	0.08	0.30	0.13	0.22	0.20	0.15	164
Taiwan_Soochow University (Taiwan)	0.08	0.05	0.46	0.19	0.19	0.18	0.20	0.51	0.35	0.25	0.43	0.41	0.16	0.26	0.16	0.49	49
Egypt_Cairo University	0.46	0.22	0.73	0.24	0.32	0.38	0.22	0.66	0.21	0.14	0.74	0.19	0.06	0.08	0.07	0.58	25
Vietnam_Can Tho University	0.07	0.04	0.00	0.13	0.36	0.27	0.11	0.00	0.00	0.03	0.08	0.05	0.02	0.14	0.50	0.19	150
Egypt_Kafrelsheikh University	0.22	0.13	0.00	0.15	0.07	0.62	0.13	0.00	0.22	0.09	0.08	0.10	0.03	0.11	0.27	0.31	118
Iraq_Al-Kunooze University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.21	0.00	0.08	0.01	0.01	0.02	0.06	0.02	191
Taiwan_Chaoyang University of Technology	0.11	0.05	0.46	0.18	0.40	0.09	0.22	0.51	0.23	0.39	0.43	0.44	0.15	0.36	0.24	0.61	17
Israel_Interdisciplinary Center Herzliya (IDC Herzliya)	0.00	0.00	0.00	0.20	0.00	0.34	0.21	0.00	0.09	0.83	0.08	0.65	0.21	0.13	0.13	0.38	86
Mexico_Universidad de Guadalajara	0.24	0.12	0.24	0.17	0.29	0.12	0.15	0.25	0.21	0.04	0.28	0.71	0.22	0.27	0.15	0.38	84

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a strong positive relationship between the two rankings.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.7009281

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 352790, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.7009281

The D9 League C

Calculating Lower D9 League C Bicluster

The next step is to identify the lower D9 league bicluster.

rmtx<-1-mtx
rres <- iBBiG(binaryMatrix=binarize(rmtx,threshold = 0.9),nModules = 1,alpha=0.33,pop_size = 100,mutation = 0.08,stagnation = 50,selection_pressure = 1.2,max_sp = 15,success_ratio = 0.8)

## Module:  1 ... done

summary(rres)

## 
## An object of class iBBiG 
## 
## There was one cluster found with Score 481.2552 and 
##   81 Rows and  15 columns

The results of the iBBiG algorithm can be seen above. The algorithm found one bicluster in which there are 81 rows (HEIs) and 15 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant.

Calculating F-tests of the Lower D9 League C Bicluster

In Table 16 the results of the row and column effects (F-tests) can be read. Both the row and column effects are significant, so the lower league bicluster is significant.

Obs.FStat <- NULL
for (i in c(1:rres@Number)){
  Obs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=rres,number=i)
}
kable(Obs.FStat,caption = "**Table 16** The results of row and column effects for the lower (D9) league")

Table 16 The results of row and column effects for the lower (D9) league

Fstat PValue Row Effect 1.867260 1.19e-05 Column Effect 8.904281 0.00e+00 Tukey test 40.489219 0.00e+00

To see the differences between those HEIs that are included in the lower league and those that are not in the lower league, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 27). (The horizontal axis of Fig. 27 shows the HEIs, the vertical axis shows the mentioned parameters on normalized (0-1) data of indicators.) On Fig. 27 the red line indicates those HEIs that are included in the lower league, while the black line shows the remaining HEIs. The HEIs in the lower league have higher means and medians, and have lower variances.

exploreBic(dset=mtx,bres=rres,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 27 Mean, median, variance and MAD for the lower D9 league HEIs

One can do the same for the columns (indicators). Fig. 28 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. (The horizontal axis of Fig. 28 shows the indicators, the vertical axis shows the mentioned parameters on normalized (0-1) data of HEIs.) The red line indicates those indicators that are in the lower league, while the black line shows the remaining indicators.

exploreBic(dset=mtx,bres=rres,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 28 Mean, median, variance and MAD for the lower D9 league indicators

Heat Maps of the Lower D9 League C

Fig. 29 depicts the heat map of the lower D9 league. The lower league contains 81 HEIs and 15 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=rres,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 29 Heat map of the lower D9 league

Fig. 30 shows the heat map of the results of iBBiG on normalized data. The lower league can be seen in the upper left corner of Fig. 30 which is enlarged on Fig. 29.

drawHeatmap(x=mtx,bicResult=rres,local=FALSE,number=1,beamercolor = TRUE,paleta=bluered(100))

Fig. 30 Heat map of the output after applying iBBiG on normalized data

Checking the Stability of the Lower D9 League C Bicluster

The next step is to check the stability of the lower league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=rres,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 0.7032474 0.7464069
##   [2,] 1.1874692 1.0833069
##   [3,] 0.8849618 0.9558872
##   [4,] 1.1390598 0.7483642
##   [5,] 0.9812189 1.0706847
##   [6,] 0.7151567 1.1188655
##   [7,] 0.8737654 1.5269216
##   [8,] 0.9616311 2.2901957
##   [9,] 1.0554031 1.1162638
##  [10,] 1.1174136 1.7363161
##  [11,] 1.2204285 1.2322497
##  [12,] 0.7546833 0.7127285
##  [13,] 0.9420437 0.7355436
##  [14,] 1.0408284 1.4258251
##  [15,] 1.1176294 1.2254485
##  [16,] 1.5159765 0.7929627
##  [17,] 1.1549281 0.6711442
##  [18,] 0.8368815 1.5087687
##  [19,] 1.0970912 0.6770413
##  [20,] 0.8662623 1.0151610
##  [21,] 1.1106314 0.8364700
##  [22,] 0.7564652 1.3454776
##  [23,] 1.0738724 1.3636523
##  [24,] 0.8364868 0.5630874
##  [25,] 1.2273524 1.6566193
##  [26,] 1.0694382 0.6877320
##  [27,] 0.7991532 1.3702375
##  [28,] 0.9204271 0.9744820
##  [29,] 1.0855557 1.0545590
##  [30,] 0.9615738 1.2290105
##  [31,] 0.7983970 1.3352289
##  [32,] 0.7979264 0.7640576
##  [33,] 1.4096926 1.3180017
##  [34,] 1.3312197 1.2498563
##  [35,] 0.8285670 0.3425553
##  [36,] 0.7258288 0.9466787
##  [37,] 1.1291998 1.3380994
##  [38,] 0.9931230 0.6299014
##  [39,] 1.0836979 0.9023672
##  [40,] 0.9751710 0.7098134
##  [41,] 0.8414710 0.6206051
##  [42,] 0.7787425 0.7709580
##  [43,] 1.1578487 1.0093464
##  [44,] 1.2147783 1.0960670
##  [45,] 1.0439317 1.5618792
##  [46,] 1.2000563 1.1553873
##  [47,] 0.8655213 1.1963632
##  [48,] 0.9309998 0.7841984
##  [49,] 1.0712610 0.3409775
##  [50,] 1.0171247 1.2205830
##  [51,] 0.6977051 0.6843781
##  [52,] 1.2985991 0.8755556
##  [53,] 1.0327833 0.7896483
##  [54,] 0.9375528 0.4902218
##  [55,] 1.2420831 1.1480930
##  [56,] 1.0442134 0.8502177
##  [57,] 1.0175186 1.8331766
##  [58,] 0.9727902 0.9186734
##  [59,] 1.0722770 1.0930672
##  [60,] 0.8434118 0.7770171
##  [61,] 0.8870630 0.9770278
##  [62,] 1.0303987 1.9930091
##  [63,] 0.9338946 1.4133610
##  [64,] 0.8381872 0.7610981
##  [65,] 0.9971178 0.8937546
##  [66,] 0.9792599 0.8961820
##  [67,] 1.2702462 0.9478229
##  [68,] 1.1592261 0.6726529
##  [69,] 0.8843483 1.5123037
##  [70,] 1.0968097 0.7226510
##  [71,] 0.8320861 1.0110031
##  [72,] 1.0275468 0.6279285
##  [73,] 1.0010709 0.6602913
##  [74,] 1.0475880 1.0352064
##  [75,] 1.1850719 1.1956692
##  [76,] 0.9133404 1.3378214
##  [77,] 1.0721714 0.4954837
##  [78,] 0.8772613 0.8900784
##  [79,] 0.9526509 0.7110851
##  [80,] 1.2595672 0.7744905
##  [81,] 0.9348948 0.6941970
##  [82,] 0.8298984 1.3320650
##  [83,] 0.9858153 0.9661053
##  [84,] 0.8401188 1.0039595
##  [85,] 1.0141174 0.7402370
##  [86,] 0.7496286 0.5602841
##  [87,] 1.1157948 0.8734773
##  [88,] 0.8841256 0.7489263
##  [89,] 0.7809472 0.9862715
##  [90,] 1.0101463 0.6222116
##  [91,] 1.1428551 1.0981614
##  [92,] 0.9451651 1.0693897
##  [93,] 0.9178380 1.3227952
##  [94,] 0.8974559 0.9428102
##  [95,] 1.4441390 0.9888856
##  [96,] 1.0394151 1.0526226
##  [97,] 1.1644815 1.1183031
##  [98,] 1.0550995 1.1196979
##  [99,] 1.2410259 0.4506769
## [100,] 1.0127154 0.6185377
## 
## $observedFstatRow
## [1] 1.86726
## 
## $observedFstatCol
## [1] 8.904281
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

The bicluster is stable.

Calculating Partial Rankings for Lower D9 League C

The next step is to calculate partial rankings based on the indicators and HEIs in the top league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR’s indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 17 shows the result of partial ranking in the case of the lower league.

C<-biclust::bicluster(mtx,rres,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 17** League C (D9) by iBBiG",digits = 2)

Table 17 League C (D9) by iBBiG

	T3	T4	T5	R1	R2	R3	R4	R5	I1	I2	I4	F1	F2	F3	F4	Overall_Score	Rank
Belarus_National Institute of Higher Education	0.12	0.00	0.19	0.00	0.05	0.00	0.00	0.15	0.00	0.00	0.26	0.94	1.00	0.00	0.98	0.56	11
Iraq_Al-Karkh University of Science	0.00	0.00	0.00	0.03	0.00	0.03	0.03	0.00	0.24	0.00	0.08	0.01	0.01	0.02	0.20	0.14	63
Iraq_University of Information Technology and Communications	0.00	0.00	0.00	0.01	0.00	0.02	0.02	0.00	0.00	0.00	0.08	0.11	0.86	0.02	0.13	0.12	68
Iraq_Al-Qasim green university Iraq	0.00	0.00	0.00	0.06	0.00	0.14	0.07	0.00	0.00	0.00	0.08	0.09	0.63	0.13	0.09	0.32	40
Russia_Mechnikov St Petersburg State Medical Academy	0.03	0.03	0.00	0.11	0.73	0.49	0.06	0.00	0.03	0.40	0.08	0.62	0.96	0.19	0.06	0.69	5
Kazakhstan_Shakarim University	0.04	0.04	0.00	0.02	0.97	0.02	0.02	0.00	0.00	0.00	0.08	0.02	0.10	0.06	0.03	0.16	61
Iraq_Hawler Medical University	0.03	0.05	0.00	0.00	0.06	0.00	0.00	0.00	0.19	0.11	0.08	0.44	0.87	0.00	0.29	0.47	17
Russia_Ufa State Aviation Technical University	0.04	0.06	0.24	0.09	0.04	0.24	0.08	0.31	0.03	0.09	0.43	0.03	0.10	0.98	0.01	0.53	14
Russia_Tver State Technical University	0.19	0.28	0.09	0.10	0.14	0.06	0.10	0.00	0.00	0.67	0.08	0.06	0.15	0.22	0.11	0.42	24
Russia_Bashkirian State Medical University	0.06	0.98	0.00	0.07	0.08	0.10	0.07	0.00	0.07	0.44	0.08	0.13	0.31	0.32	0.06	0.65	7
Russia_Kursk State Medical University	0.35	0.79	0.00	0.06	0.55	0.11	0.05	0.00	0.04	0.96	0.08	0.06	0.14	0.20	0.06	0.82	3
Pakistan_Institute of Space Technology	0.00	0.00	0.00	0.03	0.00	0.00	0.01	0.00	0.00	0.00	0.08	0.18	0.35	0.01	0.13	0.13	66
Russia_Magnitogorsk State Technical University	0.04	0.05	0.00	0.05	0.04	0.03	0.06	0.00	0.00	0.19	0.08	0.06	0.12	0.05	0.16	0.21	55
Iraq_University of AL-Qadisiyah	0.14	0.15	0.00	0.08	0.11	0.51	0.05	0.15	0.16	0.03	0.08	0.01	0.01	0.48	0.03	0.39	25
Ukraine_Poltava National Technical Yuri Kondratyuk University	0.00	0.00	0.09	0.03	0.00	0.04	0.04	0.10	0.00	0.30	0.08	0.00	0.00	0.00	0.00	0.06	76
Russia_Russian New University	0.12	0.24	0.09	0.03	0.15	0.04	0.03	0.10	0.16	0.48	0.08	0.06	0.10	0.03	0.09	0.31	43
Russia_Russian State University for the Humanities	0.11	0.08	0.49	0.05	0.05	0.06	0.09	0.47	0.24	0.31	0.48	0.00	0.00	1.00	0.01	0.71	4
Ukraine_Kyiv National Economic University	0.11	0.15	0.36	0.00	0.20	0.00	0.01	0.54	0.04	0.05	0.43	0.02	0.03	0.03	0.01	0.28	48
Russia_Ryazan State Medical University	0.13	0.31	0.09	0.03	0.95	0.04	0.04	0.00	0.13	0.65	0.08	0.09	0.13	0.08	0.07	0.36	29
Russia_Moscow State University of Design and Technology (MSUDT)	0.09	0.11	0.09	0.04	0.26	0.01	0.10	0.00	0.13	0.40	0.21	0.07	0.11	0.59	0.07	0.44	20
Iraq_Jabir Ibn Hayyan Medical University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.99	0.98	0.00	0.99	0.45	18
Russia_Don State Technical University	0.23	0.17	0.00	0.06	0.52	0.08	0.06	0.10	0.08	0.48	0.18	0.08	0.12	0.10	0.09	0.56	10
Iraq_Al-Noor University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.06	0.08	0.00	0.12	0.09	73
Kazakhstan_EA Buketov Karaganda State University	0.05	0.05	0.00	0.04	0.07	0.04	0.08	0.00	0.06	0.09	0.08	0.04	0.06	0.34	0.06	0.13	64
Iraq_Al-Kitab University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.04	0.05	0.00	0.01	0.04	80
Ukraine_Ostrogradskiy National University of Kremenchuk	0.04	0.04	0.49	0.02	0.03	0.02	0.03	0.54	0.21	0.03	0.48	0.03	0.04	0.19	0.03	0.44	21
Tunisia_Universite de la Manouba	0.24	0.35	0.00	0.17	0.04	0.16	0.17	0.00	0.14	0.07	0.08	0.05	0.07	0.98	0.03	0.34	38
Russia_Voronezh State Technical University	0.06	0.07	0.13	0.05	0.09	0.04	0.06	0.15	0.04	0.18	1.00	0.00	0.00	1.00	0.01	0.53	12
Iraq_University of Ahl al-Bayt	0.00	0.00	0.00	0.18	0.00	0.13	0.16	0.00	0.00	0.00	0.08	0.09	0.11	0.62	0.15	0.38	28
Iraq_University of Babylon	0.19	0.16	0.09	0.08	0.20	0.37	0.05	0.10	0.03	0.02	0.08	0.16	0.17	0.08	0.08	0.26	51
Iraq_University of Tikrit	0.27	0.31	0.00	0.11	0.22	0.27	0.05	0.00	0.00	0.02	0.08	0.01	0.01	1.00	0.00	0.63	8
Iraq_University of Anbar	0.18	0.22	0.00	0.09	0.80	0.29	0.07	0.00	0.05	0.00	0.08	0.15	0.16	0.09	0.12	0.43	22
Iraq_Al-Maarif University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.07	0.08	0.00	0.10	0.04	79
Russia_Ufa State Petroleum Technological University (USPTU)	0.04	0.04	0.13	0.05	0.05	0.02	0.09	0.10	0.12	0.33	0.08	0.09	0.10	0.06	0.19	0.27	49
Russia_Southwest State University	0.29	0.29	0.00	0.08	0.39	0.09	0.08	0.10	0.10	0.28	0.08	0.06	0.07	0.05	0.25	0.35	32
Russia_Tver State University	0.03	0.27	0.09	0.11	0.73	0.05	0.13	0.10	0.06	0.16	0.08	0.06	0.07	0.03	0.67	0.28	46
Russia_Volgograd State Technical University	0.09	0.10	0.00	0.09	0.16	0.02	0.11	0.00	0.03	0.36	0.08	0.10	0.11	0.11	0.25	0.35	34
Iraq_University of Misan	0.00	0.00	0.00	0.06	0.00	0.09	0.05	0.00	0.00	0.00	0.08	0.17	0.18	0.34	0.05	0.16	59
Spain_ESIC Business and Marketing School	0.00	0.00	0.00	0.04	0.00	0.10	0.04	0.00	0.73	0.58	0.08	0.28	0.33	0.11	0.06	0.38	27
Iraq_Iraq University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.57	0.00	0.08	0.08	0.09	0.00	0.04	0.11	70
Azerbaijan_Azerbaijan University of Architecture and Construction	0.17	0.15	0.00	0.02	0.73	0.03	0.03	0.10	0.24	0.43	0.08	0.05	0.06	0.20	0.03	0.51	15
Iraq_Uruk University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.16	0.00	0.08	0.01	0.01	0.00	0.02	0.03	81
Russia_Omsk State Technical University	0.17	0.19	0.09	0.07	0.75	0.06	0.09	0.00	0.04	0.74	0.18	0.07	0.07	0.09	0.16	0.68	6
Iraq_Islamic University in Najaf	0.03	0.03	0.00	0.02	0.04	0.00	0.01	0.00	0.00	0.00	0.08	0.21	0.20	0.02	0.04	0.13	65
Iraq_University of Diyala	0.14	0.14	0.00	0.06	0.42	0.30	0.04	0.00	0.00	0.00	0.08	0.02	0.02	0.58	0.03	0.32	41
Iraq_Al-Mustaqbal University College	0.00	0.00	0.00	0.08	0.00	0.23	0.05	0.00	0.22	0.00	0.08	0.16	0.15	0.04	0.20	0.28	47
Iraq_University of Thi-Qar	0.09	0.10	0.00	0.10	0.12	0.24	0.06	0.00	0.00	0.00	0.08	0.12	0.10	0.06	0.12	0.27	50
Iraq_University College in Baghdad Iraq	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.10	0.09	0.00	0.07	0.04	78
Russia_Tomsk State University of Architecture and Building	0.07	0.08	0.00	0.08	0.89	0.04	0.11	0.15	0.10	0.65	0.08	0.00	0.00	1.00	0.00	0.57	9
Iraq_Al-Nisour University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.22	0.00	0.08	0.03	0.03	0.00	0.07	0.11	71
Russia_Voronezh Institute of High Technologies	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.19	0.08	0.05	0.04	0.00	0.17	0.07	75
Russia_Pacific National University	0.09	0.07	0.00	0.04	0.18	0.03	0.07	0.00	0.09	0.30	0.08	0.09	0.07	0.06	0.14	0.29	45
Pakistan_NED University of Engineering and Technology	0.04	0.03	0.00	0.15	0.08	0.23	0.12	0.00	0.04	0.03	0.08	0.09	0.07	0.53	0.10	0.25	52
Russia_North Caucasus Federal University	0.19	0.18	0.00	0.06	0.25	0.05	0.07	0.00	0.55	0.34	0.08	0.13	0.09	0.07	0.13	0.34	39
USA_Savannah College of Art and Design	0.00	0.00	0.00	0.02	0.00	0.01	0.08	0.00	0.52	0.85	0.08	0.68	0.61	0.02	0.82	0.93	2
Russia_Ulyanovsk State University	0.10	0.11	0.00	0.13	0.04	0.08	0.15	0.00	0.06	0.44	0.08	0.11	0.08	0.30	0.20	0.38	26
Russia_Novosibirsk State University of Economics and Management	0.06	0.05	0.00	0.02	0.08	0.06	0.04	0.00	0.05	0.17	0.08	0.00	0.00	0.99	0.00	0.19	57
Kazakhstan_Suleyman Demirel University - Kazakhstan	0.00	0.00	0.00	0.61	0.00	0.17	0.92	0.00	0.56	0.24	0.08	0.02	0.02	0.99	0.04	1.00	1
Russia_Saint-Petersburg state University of Architecture and Construction	0.06	0.07	0.09	0.07	0.06	0.23	0.06	0.10	0.08	0.37	0.08	0.16	0.11	0.07	0.11	0.35	31
Azerbaijan_Azerbaijan State University of Economics (UNEC)	0.07	0.06	0.00	0.03	0.13	0.17	0.02	0.00	0.06	0.07	0.08	0.10	0.07	0.79	0.01	0.35	33
Russia_Siberian State University of Water Transport	0.08	0.09	0.00	0.10	0.08	0.08	0.10	0.00	0.12	0.17	0.08	0.14	0.10	0.15	0.16	0.31	42
Iraq_Middle Technical University	0.02	0.03	0.13	0.05	0.03	0.44	0.03	0.00	0.03	0.00	0.08	0.01	0.01	0.70	0.03	0.42	23
Russia_Rostov State University of Economics	0.11	0.06	0.00	0.01	0.08	0.02	0.02	0.00	0.07	0.15	0.08	0.05	0.03	0.02	0.06	0.13	67
Iraq_Imam Ja`afar Al-Sadiq University	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.10	0.18	0.03	0.18	0.07	0.04	0.00	0.08	0.16	60
Iraq_Al-Esraa University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.23	0.15	0.00	0.08	0.09	72
North Macedonia_European University Skopje	0.06	0.06	0.00	0.00	0.00	0.02	0.03	0.00	0.48	0.92	0.08	0.16	0.09	0.27	0.03	0.22	54
Russia_Kozma Minin Nizhny Novgorod State Pedagogical University	0.13	0.10	0.00	0.04	0.46	0.02	0.07	0.00	0.05	0.21	0.08	0.07	0.04	0.06	0.14	0.34	36
Iraq_Dijlah University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.22	0.02	0.08	0.35	0.23	0.00	0.02	0.15	62
Iraq_University of Samarra	0.05	0.00	0.00	0.02	0.04	0.09	0.02	0.00	0.00	0.00	0.08	0.03	0.03	0.46	0.02	0.08	74
Russia_Belgorod State Technological University	0.00	0.00	0.19	0.03	0.00	0.02	0.04	0.15	0.30	0.50	0.08	0.20	0.12	0.02	0.33	0.48	16
Jordan_Al-Ahliyya Amman University	0.00	0.00	0.09	0.10	0.00	0.09	0.10	0.00	0.80	0.99	0.18	0.22	0.13	0.00	0.00	0.53	13
Jordan_University of Petra (UOP)	0.00	0.00	0.00	0.14	0.00	0.13	0.12	0.00	0.62	0.87	0.08	0.09	0.04	0.27	0.14	0.45	19
Thailand_University of the Thai Chamber of Commerce	0.04	0.04	0.00	0.05	0.04	0.06	0.05	0.00	0.43	0.20	0.08	0.16	0.07	0.04	0.15	0.36	30
Iraq_University of Kirkuk	0.06	0.04	0.00	0.06	0.26	0.08	0.04	0.00	0.40	0.03	0.08	0.13	0.05	0.05	0.11	0.34	37
Iraq_Al-Farabi University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.29	0.15	0.00	0.17	0.11	69
Iraq_Southern Technical University	0.00	0.00	0.00	0.04	0.00	0.11	0.02	0.00	0.00	0.00	0.08	0.04	0.02	0.50	0.02	0.23	53
Iraq_Madenat Al-elem University College	0.00	0.00	0.00	0.02	0.00	0.08	0.02	0.00	0.31	0.00	0.08	0.04	0.02	0.04	0.05	0.18	58
Iraq_Baghdad College Of Economic Sciences University	0.00	0.00	0.00	0.04	0.00	0.03	0.04	0.00	0.00	0.00	0.08	0.17	0.06	0.97	0.01	0.35	35
Iraq_University of Alkafeel	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.34	0.00	0.08	0.30	0.13	0.00	0.22	0.20	56
Vietnam_Can Tho University	0.07	0.04	0.00	0.13	0.36	0.27	0.11	0.00	0.00	0.03	0.08	0.05	0.02	0.26	0.14	0.30	44
Iraq_Al-Kunooze University College	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.21	0.00	0.08	0.01	0.01	0.00	0.02	0.04	77

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a strong positive relationship between the two rankings.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.7256323

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 24298, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.7256323

Summary of Findings about League C

All lower leagues C satisfy all critiria, such as:

Significance: + Median C: yes + Q3 C: yes + D9 C: yes

Stability + Median C: yes + Q3 C: yes + D9 C: yes

High correlation of partial ranks + Median C: yes + Q3 C: yes + D9 C: yes

Applying BicARE on Normalized Data

With the BicARE method the middle league(s) can be specified. In order to use the BicARE method, the first step is to convert the BicARE object to a Biclust object.

bicare2biclust <- function(x){
    if(class(x)=="Biclust"){ 
        return(x)
    } else if(class(x)=="biclustering"){
        Parameters <- list(numberofbicluster=x$param[1,2],residuthreshold=x$param[2,2],genesinitialprobability=x$param[3,2],samplesinitialprobability=x$param[4,2],numberofiterations=x$param[5,2],date=x$param[6,2])
        RowxNumber <- t(x$bicRow==1)
        NumberxCol <- x$bicCol==1
        Number <- as.numeric(dim(RowxNumber)[2])
        info <- list()
        return(new("Biclust",Parameters=Parameters,RowxNumber=RowxNumber,NumberxCol=NumberxCol,Number=Number,info=info))
    }
}

In the next step the BicARE algorithm determines the number of the biclusters.

BICARE_res <- FLOC(Data=as.matrix(RUR),k=2,pGene=1,pSample=1,r=1e-3,N=280,M=10,t=10000,blocGene=NULL,blocSample=NULL)
bres <- bicare2biclust(BICARE_res)
summary(bres)

## 
## An object of class Biclust 
## 
## call:
##  NULL
## 
## Number of Clusters found:  2 
## 
## Cluster sizes:
##                    BC 1 BC 2
## Number of Rows:     280  280
## Number of Columns:   10   10

bres@Parameters$residuthreshold

## [1] "0.001"

The results above show that the BiCARE algorithm found 2 biclusters. In both bicluster there are 280 rows (HEIs) and 10 columns (indicators) which means that the first and the second bicluster are same. Because of this, in the following, only the first bicluster will be considered. This bicluster contains the middle league HEIs and indicators.

Calculating Middle League B Bicluster

The next step is to identify the middle league bicluster.

BICARE_res <- FLOC(Data=as.matrix(RUR),k=2,pGene=1,pSample=1,r=1e-3,N=280,M=10,t=10000,blocGene=NULL,blocSample=NULL)
bres <- bicare2biclust(BICARE_res)
summary(bres)

## 
## An object of class Biclust 
## 
## call:
##  NULL
## 
## Number of Clusters found:  2 
## 
## Cluster sizes:
##                    BC 1 BC 2
## Number of Rows:     280  280
## Number of Columns:   10   10

bres@Parameters$residuthreshold

## [1] "0.001"

The results of the BicARE algorithm can be seen above. The algorithm found one bicluster in which there are 280 rows (HEIs) and 10 columns (indicators). The following step is to calculate the F-tests to determine whether the bicluster is significant or not.

Calculating F-tests of the Middle League B Bicluster

In Table 20 the results of the row and column effects (F-tests) can be read. Both the row and column effects are significant, so the middle league bicluster is significant.

RObs.FStat <- NULL
for (i in c(1:bres@Number)){
  RObs.FStat[[i]] <- computeObservedFstat(x=mtx,bicResult=bres,number=i)
}
kable(RObs.FStat,caption = "**Table 20** The results of row and column effects of the middle league")

Table 20 The results of row and column effects of the middle league

Fstat PValue Row Effect 123.229656 0.0000000 Column Effect 5.459161 0.0000002 Tukey test 13.246536 0.0002786

Fstat PValue Row Effect 122.0234271 0.0000000 Column Effect 9.2526176 0.0000000 Tukey test 0.2320781 0.6300292

To see the differences between those HEIs that are included in the middle league and those that are not in the middle league, one can plot the means, medians, variances, and median absolute deviations (MAD) for rows (HEIs) (see Fig. 35). On Fig. 35 the red line indicates those HEIs that are included in the middle league, while the black line shows the remaining HEIs. Fig. 35. shows that in the case of the HEIs in the middle league the variances differ the most.

exploreBic(dset=mtx,bres=bres,mname='biclust',pfor='all',gby='genes',bnum=1)

Fig. 35 Mean, median, variance and MAD for middle league HEIs

One can do the same for the columns (indicators). Fig. 36 shows the differences between the means, medians, variances, and median absolute deviations (MAD) for the indicators. The red line indicates those indicators that are in the middle league, while the black line shows the remaining indicators. In the case of the indicators in the middle league, all parameters are different.

exploreBic(dset=mtx,bres=bres,mname='biclust',pfor='all',gby='conditions',bnum=1)

Fig. 36 Mean, median, variance and MAD for middle league indicators

Heat Maps of the Middle League B

Fig. 37 depicts the heat map of the middle league. The middle league contains 280 HEIs and 10 indicators. The red cells mean higher values in the case of indicators, while blue cells symbol lower values.

drawHeatmap(x=mtx,bicResult=bres,number=1,paleta=bluered(100),beamercolor = TRUE) 

Fig. 37 Heat map of the middle league

Fig. 38 shows the results of BicARE on normalized data. The middle league can be seen in the upper left corner of Fig. 38 which is enlarged on Fig. 37.

drawHeatmap(x=mtx,bicResult=bres,local=FALSE,number=1,paleta=bluered(100),beamercolor = TRUE) 

Fig. 14 Heat map of the output after applying BicARE on normalized data

Checking the Stability of the Middle League B Bicluster

The next step is to check the stability of the middle league bicluster. The results of the bootstrap can be seen below.

Bootstrap <- diagnoseColRow(x=as.matrix(RUR),bicResult=bres,number=1,
  nResamplings=100,replace=TRUE)
Bootstrap

## $bootstrapFstats
##         fval.row  fval.col
##   [1,] 0.9654725 1.0978251
##   [2,] 0.9748886 0.6073742
##   [3,] 1.1983284 0.6754093
##   [4,] 0.9372399 1.3475876
##   [5,] 0.9186830 0.8659411
##   [6,] 0.9535500 1.1833253
##   [7,] 1.0133518 0.9270615
##   [8,] 1.3116887 0.9446949
##   [9,] 0.9496790 0.5276194
##  [10,] 1.0090971 1.2570563
##  [11,] 0.8618730 0.5511894
##  [12,] 1.0629454 0.8349225
##  [13,] 1.0702774 0.6131635
##  [14,] 1.0519220 1.3006500
##  [15,] 0.8580317 1.6809539
##  [16,] 0.9741700 0.6839106
##  [17,] 1.0157944 1.8287388
##  [18,] 0.9953129 1.2877553
##  [19,] 0.9493655 1.5554357
##  [20,] 0.8867624 0.7627136
##  [21,] 1.1276854 1.0040383
##  [22,] 1.0598052 1.5229142
##  [23,] 1.0766962 1.3241031
##  [24,] 1.0536725 1.6902827
##  [25,] 1.0452796 1.6030843
##  [26,] 1.0438429 1.3058466
##  [27,] 1.0284492 0.9638819
##  [28,] 1.0549830 0.7033013
##  [29,] 0.9242596 0.9142408
##  [30,] 1.0229976 0.5302268
##  [31,] 1.1141205 0.4485122
##  [32,] 1.1216449 0.7787326
##  [33,] 0.9661538 1.1851329
##  [34,] 1.0663810 0.8056560
##  [35,] 0.9413381 0.9634705
##  [36,] 1.1296442 0.6987605
##  [37,] 0.9585088 1.0280077
##  [38,] 0.8921240 1.2435078
##  [39,] 1.0551398 1.8280461
##  [40,] 0.9308456 0.7427313
##  [41,] 0.9703149 0.3695467
##  [42,] 1.0610189 1.3607770
##  [43,] 0.9582506 0.9532205
##  [44,] 0.9778254 0.6116391
##  [45,] 1.0836140 0.4897520
##  [46,] 0.9376161 1.2163374
##  [47,] 1.0872887 0.9271720
##  [48,] 0.9875892 0.6884871
##  [49,] 0.8963830 1.3743197
##  [50,] 0.9763467 1.3822816
##  [51,] 1.0476048 0.5646332
##  [52,] 1.1692836 1.5436118
##  [53,] 0.9889368 2.1238246
##  [54,] 0.9998016 0.9936966
##  [55,] 0.8580025 2.1433170
##  [56,] 1.0874057 1.2912344
##  [57,] 0.9707828 0.7280606
##  [58,] 0.9105547 0.7501747
##  [59,] 0.9320128 0.4915482
##  [60,] 1.0122656 0.6458883
##  [61,] 0.9478834 1.4944715
##  [62,] 0.9779883 1.0116391
##  [63,] 1.0396465 0.4950956
##  [64,] 0.8231317 0.9547603
##  [65,] 1.0982198 1.8976780
##  [66,] 1.0084624 0.5775510
##  [67,] 0.9673208 0.4440290
##  [68,] 0.8909694 1.0436398
##  [69,] 1.1822035 0.2393775
##  [70,] 0.9076207 0.8193040
##  [71,] 1.0728258 0.2829434
##  [72,] 1.0426683 1.2188293
##  [73,] 1.0012179 0.6282573
##  [74,] 0.9846838 0.7675554
##  [75,] 0.9971417 0.2031055
##  [76,] 0.9640731 0.8999376
##  [77,] 1.1515940 0.3589734
##  [78,] 1.0159644 0.9427805
##  [79,] 0.9037804 1.4448663
##  [80,] 1.0133627 1.5003462
##  [81,] 0.9582987 1.3476056
##  [82,] 1.1145683 1.3930830
##  [83,] 1.1615162 1.2784976
##  [84,] 1.0138733 0.8191009
##  [85,] 1.1619489 1.1847403
##  [86,] 0.7925811 0.6226129
##  [87,] 0.8978420 1.0817776
##  [88,] 1.0266541 1.0144137
##  [89,] 1.1313505 0.5175151
##  [90,] 0.8473212 1.4760991
##  [91,] 1.1247006 0.9974105
##  [92,] 1.1616582 1.0581748
##  [93,] 1.0904371 1.6326500
##  [94,] 0.9886459 0.7337353
##  [95,] 1.3109860 1.4120835
##  [96,] 1.1266580 0.4169031
##  [97,] 1.1004420 0.7601623
##  [98,] 0.9470697 0.6361148
##  [99,] 0.9469009 0.4247412
## [100,] 1.0560269 0.3167390
## 
## $observedFstatRow
## [1] 123.2297
## 
## $observedFstatCol
## [1] 5.459161
## 
## $bootstrapPvalueRow
## [1] 0
## 
## $bootstrapPvalueCol
## [1] 0

Since the bootstrapPvalueRow and the bootstrapPvalueCol are lower than 0.01, the bicluster is stable.

Calculating Partial Rankings

The next step is to calculate partial rankings based on the indicators and HEIs in the middle league. The calculation of each score of each indicator of the HEIs are done according to the method used in the original RUR ranking. The original weights of RUR’s indicators are used, and the total scores for the HEIs are calculated using the selected indicators in the given bicluster. Table 21 shows the result of partial ranking in the case of the middle league.

C<-biclust::bicluster(mtx,bres,number=1)
B<-as.data.frame(C[[1]])
selectedweight<-weights[,colnames(B)]
cols <- colnames(B)
sw<-weights[,cols]
BR<-rowSums(B[,cols]*sw)/max(rowSums(B[,cols]*sw))
B$Overall_Score<-BR
B$Rank<-rank(-B$Overall_Score)
kable(B,caption = "**Table 21** League B by BicARE",digits = 2)

Table 21 League B by BicARE

	T5	R1	R3	R4	R5	I1	I4	I5	F1	F4	Overall_Score	Rank
Iraq_Al-Karkh University of Science	0.00	0.03	0.03	0.03	0.00	0.24	0.08	0.32	0.01	0.20	0.10	197
Iraq_University of Information Technology and Communications	0.00	0.01	0.02	0.02	0.00	0.00	0.08	0.26	0.11	0.13	0.07	217
Iraq_Al-Qasim green university Iraq	0.00	0.06	0.14	0.07	0.00	0.00	0.08	0.26	0.09	0.09	0.08	207
USA_Emory University	0.90	0.80	0.92	0.66	0.89	0.67	0.87	0.67	0.95	0.80	0.84	34
Kazakhstan_Shakarim University	0.00	0.02	0.02	0.02	0.00	0.00	0.08	0.25	0.02	0.03	0.05	232
USA_Johns Hopkins University	0.98	0.92	0.95	0.85	0.98	0.75	0.98	0.79	0.96	0.99	0.24	96
USA_University of Rochester	0.76	0.79	0.89	0.66	0.79	0.71	0.82	0.74	0.97	0.82	0.21	132
USA_Yale University	0.99	0.95	0.96	0.90	0.99	0.78	0.99	0.77	0.98	0.87	0.24	95
USA_Columbia University	0.99	0.84	0.97	0.68	0.98	0.81	0.98	0.84	0.89	0.83	0.23	111
USA_University of Chicago	0.98	0.99	0.99	0.93	0.99	0.81	0.99	0.80	0.96	0.83	0.24	92
USA_California Institute of Technology (Caltech)	0.99	1.00	0.99	0.99	0.99	0.85	0.99	0.91	0.99	0.94	1.00	1
USA_University of Pennsylvania	0.98	0.93	0.95	0.87	0.98	0.80	0.97	0.74	0.99	0.86	0.94	12
Denmark_Technical University of Denmark	0.79	0.82	0.80	0.76	0.82	0.96	0.84	0.91	0.56	0.91	0.85	33
Japan_Gifu University	0.29	0.36	0.16	0.44	0.20	0.55	0.48	0.35	0.21	0.28	0.35	78
USA_Stanford University	1.00	0.97	0.99	0.87	1.00	0.90	1.00	0.83	0.99	0.85	0.97	2
Japan_Tottori University	0.09	0.33	0.16	0.40	0.10	0.31	0.21	0.18	0.25	0.18	0.06	221
USA_Washington University in St. Louis	0.93	0.94	0.97	0.85	0.93	0.69	0.91	0.68	0.96	0.85	0.23	114
Japan_Okayama University	0.46	0.53	0.34	0.54	0.51	0.32	0.64	0.41	0.48	0.43	0.12	184
USA_University of California, Los Angeles	0.99	0.86	0.93	0.76	0.99	0.74	0.99	0.74	0.92	0.80	0.23	112
Russia_Tver State Technical University	0.09	0.10	0.06	0.10	0.00	0.00	0.08	0.30	0.06	0.11	0.02	262
USA_Princeton University	0.99	0.96	0.99	0.88	0.99	0.86	0.99	0.85	0.97	0.85	0.97	4
Russia_Bashkirian State Medical University	0.00	0.07	0.10	0.07	0.00	0.07	0.08	0.18	0.13	0.06	0.08	210
Russia_Kursk State Medical University	0.00	0.06	0.11	0.05	0.00	0.04	0.08	0.31	0.06	0.06	0.08	211
USA_University of Michigan	0.99	0.85	0.89	0.78	0.99	0.74	0.98	0.72	0.83	0.82	0.89	25
Ukraine_National Technical University Kharkiv Polytechnic Institute	0.19	0.08	0.08	0.08	0.35	0.08	0.21	0.34	0.02	0.04	0.15	169
Russia_Siberian State Medical University	0.00	0.12	0.15	0.12	0.00	0.10	0.08	0.26	0.14	0.10	0.03	251
India_Manipal Academy of Higher Education	0.43	0.17	0.17	0.18	0.44	0.40	0.60	0.44	0.21	0.25	0.09	203
USA_Massachusetts Institute of Technology (MIT)	1.00	0.90	1.00	0.62	1.00	0.93	1.00	0.92	0.99	0.93	0.24	91
Argentina_Austral University (Argentina)	0.19	0.14	0.31	0.11	0.35	0.32	0.48	0.44	0.14	0.05	0.07	219
USA_Rice University	0.85	0.90	0.98	0.79	0.84	0.79	0.86	0.80	0.88	0.75	0.22	120
Sweden_Karolinska Institute	0.92	0.99	0.91	0.98	0.93	0.72	0.95	0.87	0.84	0.97	0.94	11
USA_Harvard University	1.00	1.00	0.98	1.00	1.00	0.75	1.00	0.80	0.97	0.87	0.97	3
Russia_Kazan National Research Technical University named after A.N. Tupolev	0.19	0.09	0.06	0.12	0.10	0.27	0.18	0.26	0.20	0.47	0.20	141
Japan_Kobe University	0.61	0.54	0.37	0.58	0.61	0.46	0.43	0.37	0.56	0.56	0.53	62
India_Jamia Millia Islamia	0.13	0.17	0.31	0.14	0.10	0.25	0.18	0.24	0.20	0.09	0.19	153
Pakistan_Institute of Space Technology	0.00	0.03	0.00	0.01	0.00	0.00	0.08	0.26	0.18	0.13	0.02	268
Japan_Chiba University	0.33	0.52	0.30	0.57	0.31	0.33	0.35	0.29	0.30	0.47	0.10	196
China_Harbin Institute of Technology	0.64	0.58	0.60	0.67	0.69	0.56	0.67	0.49	0.68	0.90	0.17	163
USA_Cornell University	0.97	0.96	0.94	0.93	0.97	0.82	0.98	0.79	0.83	0.80	0.23	101
Russia_Magnitogorsk State Technical University	0.00	0.05	0.03	0.06	0.00	0.00	0.08	0.07	0.06	0.16	0.01	273
USA_Drexel University	0.60	0.56	0.81	0.42	0.57	0.64	0.66	0.59	0.60	0.42	0.61	58
Japan_Osaka Prefecture University	0.24	0.44	0.20	0.48	0.51	0.36	0.48	0.28	0.29	0.35	0.38	73
Iraq_University of AL-Qadisiyah	0.00	0.08	0.51	0.05	0.15	0.16	0.08	0.31	0.01	0.03	0.14	174
Ukraine_Kharkiv National University of Radio Electronics	0.13	0.07	0.21	0.05	0.31	0.04	0.08	0.29	0.03	0.04	0.13	181
UK_University College London	0.97	0.90	0.94	0.84	0.97	0.92	0.98	0.97	0.66	0.69	0.91	16
Russia_Altai State University	0.09	0.12	0.18	0.12	0.10	0.36	0.08	0.40	0.08	0.19	0.04	234
Ukraine_Poltava National Technical Yuri Kondratyuk University	0.09	0.03	0.04	0.04	0.10	0.00	0.08	0.09	0.00	0.00	0.01	274
Iraq_University of Baghdad	0.33	0.07	0.20	0.05	0.31	0.17	0.18	0.30	0.13	0.05	0.05	233
USA_State University of New York, Stony Brook	0.68	0.60	0.82	0.50	0.74	0.78	0.75	0.73	0.63	0.53	0.18	160
Romania_Grigore T. Popa University of Medicine and Pharmacy	0.13	0.31	0.20	0.38	0.00	0.03	0.08	0.29	0.11	0.04	0.04	236
Russia_Perm State University	0.19	0.12	0.04	0.15	0.15	0.12	0.08	0.07	0.08	0.16	0.12	182
UK_University of Oxford	0.99	0.91	0.98	0.81	0.99	0.91	0.99	0.97	0.87	0.73	0.95	9
Iraq_Mustansiriyah University	0.13	0.05	0.17	0.03	0.15	0.05	0.08	0.26	0.12	0.01	0.11	189
Russia_Kazan National Research Technological University	0.09	0.11	0.05	0.13	0.00	0.08	0.08	0.17	0.12	0.31	0.12	185
China_Jilin University	0.24	0.43	0.39	0.41	0.20	0.30	0.32	0.21	0.31	0.51	0.34	79
USA_Brown University	0.90	0.97	0.92	0.96	0.91	0.76	0.91	0.71	0.93	0.75	0.23	113
USA_Lehigh University	0.51	0.51	0.49	0.51	0.44	0.38	0.64	0.52	0.71	0.45	0.13	180
Russia_Russian New University	0.09	0.03	0.04	0.03	0.10	0.16	0.08	0.17	0.06	0.09	0.02	264
Russia_Moscow Pedagogical State University	0.24	0.09	0.07	0.09	0.10	0.11	0.21	0.26	0.10	0.08	0.04	243
Tunisia_Universite de Carthage	0.00	0.16	0.17	0.17	0.10	0.13	0.08	0.29	0.01	0.02	0.03	247
Russia_Voronezh State University	0.19	0.13	0.07	0.16	0.31	0.23	0.43	0.33	0.07	0.12	0.21	129
Hong Kong_City University of Hong Kong	0.78	0.87	0.86	0.92	0.82	0.99	0.76	0.79	1.00	0.82	0.89	23
Republic of Korea_Kookmin University	0.09	0.22	0.26	0.18	0.15	0.38	0.21	0.29	0.17	0.32	0.24	97
UK_University of Cambridge	1.00	0.92	0.96	0.82	1.00	0.88	0.99	0.96	0.94	0.73	0.95	8
China_Shanghai Jiao Tong University	0.80	0.82	0.49	0.92	0.82	0.75	0.82	0.61	0.87	0.96	0.82	40
Russia_Saratov State University	0.24	0.21	0.15	0.22	0.25	0.08	0.18	0.24	0.16	0.44	0.06	223
USA_University of Washington	0.97	0.89	0.97	0.78	0.97	0.73	0.96	0.71	0.94	0.89	0.23	109
USA_University of Illinois at Chicago	0.84	0.75	0.74	0.69	0.85	0.67	0.87	0.66	0.84	0.63	0.20	146
Russia_Moscow Institute of Physics and Technology	0.88	0.65	0.48	0.72	0.84	0.74	0.70	0.70	0.70	0.79	0.19	156
China_Fudan University	0.83	0.87	0.61	0.91	0.83	0.64	0.77	0.56	0.85	0.97	0.20	137
Russia_Ryazan State Medical University	0.09	0.03	0.04	0.04	0.00	0.13	0.08	0.22	0.09	0.07	0.08	205
Switzerland_Ecole Polytechnique Federale de Lausanne	0.94	0.90	0.97	0.73	0.95	0.99	0.95	1.00	0.79	0.87	0.94	10
Russia_Moscow State University of Design and Technology (MSUDT)	0.09	0.04	0.01	0.10	0.00	0.13	0.21	0.18	0.07	0.07	0.09	201
UK_Imperial College London	0.98	0.96	0.95	0.92	0.98	0.93	0.98	0.99	0.86	0.76	0.97	6
China_Peking University	0.95	0.83	0.71	0.84	0.95	0.82	0.93	0.71	0.98	0.97	0.90	21
Estonia_University of Tartu	0.63	0.59	0.75	0.48	0.57	0.47	0.60	0.60	0.38	0.56	0.15	173
USA_Boston University	0.91	0.87	0.94	0.77	0.90	0.64	0.93	0.74	0.82	0.77	0.22	124
Russia_Bashkir State University	0.13	0.15	0.08	0.16	0.10	0.03	0.08	0.08	0.07	0.16	0.03	253
USA_University of Southern California	0.93	0.83	0.87	0.74	0.93	0.71	0.93	0.74	0.93	0.78	0.22	122
Russia_Volgograd State University	0.00	0.10	0.03	0.12	0.00	0.14	0.08	0.11	0.07	0.09	0.02	267
South Africa_University of Cape Town	0.78	0.71	0.80	0.68	0.77	0.82	0.75	0.82	0.58	0.73	0.77	44
Russia_Irkutsk State University	0.24	0.13	0.15	0.13	0.15	0.15	0.08	0.17	0.06	0.10	0.14	176
China_Tsinghua University	0.96	0.83	0.75	0.84	0.96	0.73	0.95	0.64	0.96	0.99	0.89	24
USA_University of California, Davis	0.94	0.78	0.82	0.71	0.95	0.76	0.95	0.72	0.93	0.83	0.87	28
Poland_Lodz University of Technology	0.13	0.26	0.16	0.32	0.15	0.15	0.08	0.16	0.19	0.25	0.19	149
USA_North Carolina State University	0.86	0.65	0.65	0.67	0.85	0.81	0.88	0.69	0.81	0.76	0.20	145
Russia_Don State Technical University	0.00	0.06	0.08	0.06	0.10	0.08	0.18	0.29	0.08	0.09	0.03	256
Russia_Northern (Arctic) Federal University (NArFU)	0.00	0.07	0.05	0.09	0.00	0.20	0.08	0.12	0.12	0.18	0.02	261
Azerbaijan_Baku State University	0.13	0.10	0.09	0.10	0.31	0.23	0.43	0.37	0.02	0.07	0.05	231
Sweden_Chalmers University of Technology	0.75	0.73	0.54	0.78	0.76	0.87	0.73	0.82	0.63	0.92	0.20	148
USA_Ohio State University	0.94	0.71	0.84	0.63	0.94	0.84	0.94	0.71	0.94	0.75	0.85	31
Iraq_Al-Noor University College	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.06	0.12	0.03	252
Kazakhstan_EA Buketov Karaganda State University	0.00	0.04	0.04	0.08	0.00	0.06	0.08	0.13	0.04	0.06	0.06	224
Hungary_University of Szeged	0.29	0.38	0.49	0.34	0.20	0.39	0.24	0.49	0.41	0.31	0.37	75
Norway_University of Bergen	0.65	0.85	0.90	0.79	0.64	0.80	0.64	0.77	0.56	0.56	0.74	45
Russia_Samara University	0.19	0.16	0.07	0.16	0.25	0.05	0.35	0.18	0.10	0.21	0.04	235
Iraq_Al-Kitab University	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.04	0.01	0.00	280
USA_Northwestern University	0.96	0.97	0.97	0.94	0.96	0.79	0.96	0.73	0.97	0.93	0.24	94
China_Hangzhou Dianzi University	0.13	0.29	0.52	0.27	0.15	0.29	0.30	0.18	0.19	0.30	0.07	216
Canada_McGill University	0.95	0.91	0.80	0.89	0.94	0.86	0.96	0.90	0.60	0.78	0.22	118
Tunisia_Universite de la Manouba	0.00	0.17	0.16	0.17	0.00	0.14	0.08	0.27	0.05	0.03	0.11	188
USA_George Washington University	0.79	0.60	0.79	0.56	0.78	0.68	0.83	0.65	0.80	0.64	0.74	46
USA_University of Connecticut	0.65	0.61	0.60	0.64	0.71	0.76	0.76	0.58	0.89	0.61	0.71	53
Ukraine_South Ukrainian National Pedagogical University named after K.D. Ushynsky	0.13	0.05	0.07	0.06	0.25	0.18	0.24	0.41	0.03	0.04	0.15	170
Russia_Tyumen State University	0.09	0.13	0.23	0.14	0.10	0.26	0.08	0.32	0.18	0.32	0.19	151
Switzerland_ETH Zurich (Swiss Federal Institute of Technology)	0.98	0.96	0.93	0.94	0.98	0.99	0.98	1.00	0.84	0.96	0.25	89
Russia_Belgorod National Research University	0.19	0.15	0.32	0.14	0.15	0.21	0.08	0.38	0.14	0.35	0.05	226
China_Beijing Jiaotong University	0.40	0.39	0.41	0.43	0.40	0.28	0.53	0.36	0.41	0.69	0.11	187
USA_Carnegie Mellon University	0.96	0.88	0.91	0.82	0.96	0.83	0.97	0.86	0.92	0.95	0.23	98
USA_University of Notre Dame	0.81	0.81	0.79	0.79	0.82	0.79	0.83	0.67	0.87	0.72	0.21	134
Netherlands_University of Twente	0.74	0.84	0.58	0.90	0.79	0.86	0.82	0.86	0.74	0.94	0.83	36
UK_University of Bristol	0.86	0.92	0.96	0.81	0.86	0.84	0.89	0.84	0.63	0.62	0.85	32
Russia_Immanuel Kant Baltic Federal University	0.19	0.14	0.11	0.15	0.20	0.17	0.08	0.27	0.15	0.15	0.17	164
Poland_University of Lodz	0.09	0.22	0.20	0.23	0.15	0.19	0.21	0.23	0.08	0.14	0.18	158
Iraq_University of Ahl al-Bayt	0.00	0.18	0.13	0.16	0.00	0.00	0.08	0.17	0.09	0.15	0.10	194
Russia_Samara State Technical University	0.13	0.11	0.06	0.12	0.15	0.05	0.24	0.09	0.13	0.26	0.03	244
China_Wuhan University of Science & Technology	0.09	0.20	0.34	0.20	0.10	0.25	0.21	0.14	0.14	0.28	0.05	228
Iraq_University of Babylon	0.09	0.08	0.37	0.05	0.10	0.03	0.08	0.27	0.16	0.08	0.03	245
USA_University of California, Berkeley	0.99	0.94	0.98	0.82	0.99	0.80	0.99	0.80	0.89	0.83	0.23	99
Denmark_Aarhus University	0.78	0.90	0.76	0.91	0.80	0.85	0.81	0.76	0.54	0.89	0.21	130
UK_Newcastle University	0.69	0.67	0.84	0.62	0.67	0.83	0.79	0.83	0.49	0.62	0.73	48
Iraq_University of Tikrit	0.00	0.11	0.27	0.05	0.00	0.00	0.08	0.26	0.01	0.00	0.08	206
Spain_University of Navarra	0.70	0.62	0.69	0.58	0.61	0.60	0.64	0.65	0.68	0.56	0.66	56
Iraq_University of Anbar	0.00	0.09	0.29	0.07	0.00	0.05	0.08	0.27	0.15	0.12	0.12	186
Iraq_Al-Maarif University College	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.07	0.10	0.03	254
Russia_Ufa State Petroleum Technological University (USPTU)	0.13	0.05	0.02	0.09	0.10	0.12	0.08	0.13	0.09	0.19	0.03	259
Russia_Southwest State University	0.00	0.08	0.09	0.08	0.10	0.10	0.08	0.16	0.06	0.25	0.03	257
Poland_Gdansk University of Technology	0.19	0.29	0.26	0.32	0.15	0.15	0.08	0.16	0.24	0.33	0.06	222
Republic of Korea_Yeungnam University	0.19	0.44	0.38	0.50	0.20	0.56	0.30	0.35	0.36	0.41	0.10	199
Russia_Volgograd State Technical University	0.00	0.09	0.02	0.11	0.00	0.03	0.08	0.11	0.10	0.25	0.02	266
Finland_University of Jyvaskyla	0.36	0.47	0.58	0.45	0.40	0.43	0.38	0.49	0.37	0.63	0.47	65
Chile_Pontificia University Catolica de Chile	0.74	0.53	0.52	0.50	0.68	0.60	0.69	0.65	0.47	0.69	0.63	57
Slovenia_University of Maribor	0.19	0.35	0.38	0.39	0.15	0.17	0.08	0.26	0.18	0.29	0.25	87
Iraq_University of Misan	0.00	0.06	0.09	0.05	0.00	0.00	0.08	0.26	0.17	0.05	0.08	212
Japan_University of Electro-Communications	0.24	0.42	0.19	0.55	0.31	0.49	0.32	0.38	0.36	0.48	0.39	72
UK_University of York	0.72	0.81	0.83	0.75	0.75	0.82	0.81	0.79	0.54	0.53	0.19	152
Taiwan_National Chung Hsing University	0.40	0.36	0.20	0.41	0.57	0.33	0.48	0.29	0.36	0.60	0.10	192
Azerbaijan_Azerbaijan University of Architecture and Construction	0.00	0.02	0.03	0.03	0.10	0.24	0.08	0.29	0.05	0.03	0.02	263
Iraq_Uruk University	0.00	0.00	0.00	0.00	0.00	0.16	0.08	0.04	0.01	0.02	0.01	277
China_Nanjing University	0.72	0.85	0.65	0.87	0.71	0.98	0.69	0.61	0.80	0.90	0.20	140
Switzerland_University of Geneva	0.78	0.95	0.92	0.91	0.77	0.95	0.79	0.94	0.62	0.68	0.86	29
Sweden_Royal Institute of Technology (KTH)	0.88	0.83	0.62	0.87	0.88	0.91	0.91	0.90	0.69	0.90	0.87	27
China_China Pharmaceutical University	0.36	0.34	0.39	0.32	0.25	0.10	0.26	0.12	0.40	0.34	0.30	83
Croatia_University of Rijeka	0.00	0.20	0.26	0.19	0.15	0.07	0.08	0.18	0.12	0.08	0.14	178
Thailand_Prince of Songkla University	0.40	0.21	0.20	0.20	0.47	0.33	0.43	0.34	0.42	0.18	0.33	80
Singapore_Nanyang Technological University	0.94	0.93	0.96	0.89	0.94	0.97	0.92	0.94	0.93	0.92	0.24	90
Norway_Norwegian University of Science and Technology	0.76	0.53	0.53	0.54	0.78	0.71	0.80	0.68	0.54	0.61	0.17	165
Russia_Omsk State Technical University	0.09	0.07	0.06	0.09	0.00	0.04	0.18	0.26	0.07	0.16	0.03	258
Germany_Ruprecht Karl University of Heidelberg	0.90	0.86	0.94	0.75	0.88	0.59	0.89	0.76	0.76	0.64	0.21	131
Spain_University of Vigo	0.36	0.34	0.39	0.35	0.20	0.14	0.56	0.40	0.25	0.24	0.08	204
USA_University of South Carolina	0.49	0.57	0.66	0.55	0.60	0.67	0.60	0.51	0.63	0.57	0.60	59
USA_Oregon State University	0.74	0.68	0.66	0.63	0.74	0.74	0.79	0.62	0.75	0.72	0.73	47
Mexico_Monterrey Institute of Technology and Higher Education	0.53	0.26	0.32	0.27	0.35	0.59	0.56	0.60	0.43	0.57	0.47	66
Japan_Kyushu Institute of Technology	0.46	0.46	0.28	0.54	0.31	0.46	0.60	0.40	0.33	0.39	0.44	68
Iraq_Islamic University in Najaf	0.00	0.02	0.00	0.01	0.00	0.00	0.08	0.00	0.21	0.04	0.04	242
Finland_University of Turku	0.55	0.71	0.62	0.71	0.47	0.46	0.56	0.56	0.44	0.43	0.14	175
Canada_University of Calgary	0.75	0.83	0.72	0.83	0.75	0.80	0.83	0.77	0.68	0.77	0.20	142
Iraq_University of Diyala	0.00	0.06	0.30	0.04	0.00	0.00	0.08	0.26	0.02	0.03	0.02	265
USA_University of California, Irvine	0.82	0.82	0.92	0.70	0.86	0.77	0.86	0.76	0.94	0.76	0.21	128
USA_University of Tennessee Knoxville	0.61	0.72	0.84	0.68	0.54	0.68	0.60	0.51	0.83	0.58	0.17	162
Turkey_Atilim University	0.13	0.19	0.32	0.21	0.10	0.29	0.28	0.33	0.21	0.16	0.23	107
Iraq_Al-Mustaqbal University College	0.00	0.08	0.23	0.05	0.00	0.22	0.08	0.32	0.16	0.20	0.14	177
Romania_George Emil Palade University of Medicine, Pharmacy, Science, and Technology of Targu Mures	0.00	0.17	0.12	0.16	0.00	0.11	0.08	0.18	0.14	0.04	0.10	191
Taiwan_National Taipei University	0.29	0.19	0.22	0.23	0.31	0.17	0.48	0.26	0.23	0.25	0.27	84
USA_Michigan State University	0.93	0.72	0.79	0.72	0.92	0.81	0.94	0.73	0.88	0.81	0.86	30
USA_University of Delaware	0.69	0.68	0.76	0.61	0.73	0.66	0.76	0.59	0.80	0.99	0.19	154
USA_Purdue University	0.95	0.86	0.68	0.83	0.95	0.89	0.96	0.79	0.83	0.90	0.22	117
USA_University of Nebraska	0.72	0.65	0.74	0.64	0.66	0.77	0.67	0.62	0.78	0.74	0.18	157
Russia_South Ural State University	0.19	0.11	0.11	0.11	0.15	0.11	0.18	0.19	0.11	0.23	0.04	239
Brazil_Universidade Federal do Ceara	0.24	0.27	0.26	0.30	0.15	0.25	0.21	0.19	0.40	0.27	0.07	218
Iraq_University of Thi-Qar	0.00	0.10	0.24	0.06	0.00	0.00	0.08	0.25	0.12	0.12	0.10	195
Iraq_University College in Baghdad Iraq	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.10	0.07	0.03	255
Russia_Tomsk State University of Architecture and Building	0.00	0.08	0.04	0.11	0.15	0.10	0.08	0.21	0.00	0.00	0.08	208
Iraq_Al-Nisour University College	0.00	0.00	0.00	0.00	0.00	0.22	0.08	0.06	0.03	0.07	0.05	230
Canada_Laval University	0.60	0.72	0.62	0.72	0.61	0.81	0.76	0.70	0.57	0.79	0.72	51
USA_State University of New York, Buffalo	0.61	0.68	0.71	0.67	0.67	0.83	0.73	0.68	0.76	0.87	0.19	155
Netherlands_Radboud University Nijmegen	0.64	0.97	0.88	0.95	0.72	0.72	0.74	0.75	0.67	0.85	0.20	135
Russia_Voronezh Institute of High Technologies	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.05	0.05	0.17	0.01	276
USA_Colorado State University	0.76	0.51	0.65	0.45	0.75	0.57	0.76	0.51	0.73	0.65	0.16	167
Australia_Australian National University	0.91	0.94	0.89	0.95	0.93	0.97	0.94	0.96	0.82	0.93	0.24	93
Singapore_National University of Singapore	0.98	0.89	0.82	0.87	0.98	0.98	0.96	0.96	0.97	0.92	0.97	5
Portugal_University of Minho	0.51	0.46	0.58	0.40	0.44	0.34	0.53	0.55	0.23	0.31	0.45	67
USA_George Mason University	0.57	0.46	0.67	0.39	0.57	0.69	0.60	0.54	0.63	0.50	0.58	60
USA_Washington State University	0.67	0.64	0.73	0.62	0.63	0.72	0.72	0.56	0.77	0.86	0.72	50
Hong Kong_University of Hong Kong	0.94	0.95	0.77	0.97	0.93	0.99	0.92	0.87	0.95	0.97	0.96	7
USA_Old Dominion University	0.43	0.42	0.65	0.39	0.35	0.41	0.53	0.39	0.69	0.43	0.12	183
Russia_Pacific National University	0.00	0.04	0.03	0.07	0.00	0.09	0.08	0.14	0.09	0.14	0.02	269
USA_Virginia Polytechnic Institute and State University	0.87	0.60	0.55	0.66	0.87	0.76	0.88	0.67	0.79	0.89	0.20	147
Pakistan_NED University of Engineering and Technology	0.00	0.15	0.23	0.12	0.00	0.04	0.08	0.27	0.09	0.10	0.03	249
Canada_University of British Columbia	0.96	0.92	0.86	0.90	0.96	0.94	0.97	0.93	0.78	0.77	0.23	103
Finland_Aalto University	0.77	0.86	0.73	0.85	0.79	0.71	0.80	0.84	0.64	0.63	0.79	43
Hong Kong_Chinese University Hong Kong	0.89	0.95	0.82	0.97	0.89	0.97	0.82	0.81	0.95	0.95	0.93	15
USA_Oakland University	0.33	0.33	0.40	0.35	0.25	0.39	0.35	0.31	0.55	0.13	0.35	76
Croatia_University of Zagreb	0.46	0.26	0.27	0.28	0.40	0.12	0.24	0.25	0.17	0.15	0.27	86
USA_Mississippi State University	0.29	0.52	0.40	0.55	0.20	0.35	0.32	0.26	0.39	0.57	0.40	71
Russia_Ulyanovsk State University	0.00	0.13	0.08	0.15	0.00	0.06	0.08	0.19	0.11	0.20	0.03	260
Russia_Novosibirsk State University of Economics and Management	0.00	0.02	0.06	0.04	0.00	0.05	0.08	0.06	0.00	0.00	0.01	278
Taiwan_Yuan Ze University	0.29	0.38	0.17	0.52	0.31	0.34	0.30	0.28	0.38	0.51	0.09	202
Republic of Korea_Sungkyunkwan University	0.96	0.93	0.57	0.96	0.96	0.73	0.92	0.64	0.91	0.95	0.22	119
North Macedonia_University of Sarajevo	0.00	0.17	0.42	0.14	0.00	0.13	0.08	0.33	0.12	0.06	0.04	241
USA_University of South Florida	0.55	0.74	0.61	0.75	0.66	0.69	0.69	0.59	0.76	0.91	0.72	49
Mexico_Metropolitan Autonomous University	0.24	0.18	0.27	0.16	0.35	0.44	0.60	0.33	0.29	0.49	0.35	77
UK_University of Strathclyde	0.61	0.55	0.63	0.57	0.61	0.84	0.70	0.80	0.53	0.55	0.66	55
Canada_University of Toronto	0.97	0.94	0.87	0.92	0.97	0.87	0.98	0.86	0.82	0.84	0.94	13
Czech Republic_Masaryk University	0.58	0.46	0.33	0.51	0.47	0.51	0.56	0.62	0.30	0.68	0.52	63
Canada_Universite de Montreal	0.80	0.89	0.69	0.91	0.81	0.86	0.86	0.82	0.79	0.84	0.21	125
Russia_Saint-Petersburg state University of Architecture and Construction	0.09	0.07	0.23	0.06	0.10	0.08	0.08	0.14	0.16	0.11	0.03	248
Netherlands_Erasmus University Rotterdam	0.85	0.99	0.92	0.97	0.87	0.83	0.88	0.84	0.72	0.94	0.23	110
Azerbaijan_Azerbaijan State University of Economics (UNEC)	0.00	0.03	0.17	0.02	0.00	0.06	0.08	0.07	0.10	0.01	0.01	271
USA_Texas Tech University	0.55	0.56	0.61	0.57	0.47	0.73	0.60	0.55	0.71	0.35	0.15	172
Spain_University of Seville	0.55	0.36	0.39	0.38	0.54	0.26	0.48	0.39	0.24	0.27	0.40	70
Australia_University of Sydney	0.93	0.93	0.85	0.94	0.93	0.83	0.95	0.89	0.74	0.74	0.90	20
Russia_Siberian State University of Water Transport	0.00	0.10	0.08	0.10	0.00	0.12	0.08	0.13	0.14	0.16	0.09	200
Taiwan_Tatung University	0.00	0.31	0.14	0.36	0.00	0.12	0.08	0.08	0.26	0.31	0.17	161
Taiwan_Fu Jen Catholic University	0.36	0.27	0.21	0.29	0.35	0.42	0.43	0.35	0.33	0.60	0.37	74
Iraq_Middle Technical University	0.13	0.05	0.44	0.03	0.00	0.03	0.08	0.27	0.01	0.03	0.03	250
USA_Arizona State University	0.89	0.69	0.71	0.69	0.89	0.72	0.91	0.72	0.82	0.69	0.20	143
China_Guizhou University	0.00	0.20	0.30	0.19	0.00	0.14	0.08	0.09	0.27	0.29	0.04	237
Netherlands_Wageningen University and Research Center	0.90	0.90	0.94	0.84	0.91	0.67	0.93	0.87	0.91	0.95	0.23	108
Netherlands_Tilburg University	0.64	0.76	0.67	0.91	0.71	0.82	0.75	0.73	0.74	0.95	0.20	144
Thailand_King Mongkuts University of Technology Thonburi | 0.40| 0.25| 0.34| 0.26| 0.40| 0.38| 0.60| 0.40| 0.46| 0.62| 0.43| 69| |USA_University of Texas at Dallas | 0.63| 0.69| 0.76| 0.62| 0.71| 0.50| 0.78| 0.69| 0.67| 0.46| 0.67| 54| |Russia_Rostov State University of Economics | 0.00| 0.01| 0.02| 0.02| 0.00| 0.07| 0.08| 0.06| 0.05| 0.06| 0.04| 240| |Ireland_Trinity College Dublin | 0.78| 0.85| 0.81| 0.80| 0.77| 0.94| 0.81| 0.90| 0.67| 0.73| 0.84| 35| |Iraq_Imam Jaafar Al-Sadiq University	0.00	0.00	0.00	0.00	0.10	0.18	0.18	0.08	0.07	0.08	0.07	215
South Africa_University of Pretoria	0.57	0.43	0.34	0.55	0.51	0.62	0.43	0.54	0.58	0.66	0.14	179
Iraq_Al-Esraa University College	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.23	0.08	0.01	275
Mexico_Autonomous University of Mexico State	0.24	0.12	0.11	0.12	0.25	0.18	0.35	0.22	0.27	0.17	0.05	227
Taiwan_Ming Chuan University	0.00	0.16	0.12	0.18	0.10	0.40	0.18	0.29	0.25	0.23	0.05	229
Thailand_Kasetsart University	0.46	0.19	0.19	0.18	0.51	0.35	0.48	0.39	0.46	0.53	0.10	198
Brazil_Pontificia Universidade Catolica do Rio Grande do Sul	0.24	0.22	0.28	0.21	0.10	0.20	0.18	0.19	0.39	0.41	0.25	88
Canada_Western University	0.67	0.86	0.64	0.92	0.66	0.92	0.76	0.75	0.79	0.76	0.80	42
Hong Kong_Hong Kong Polytechnic University	0.82	0.66	0.75	0.73	0.86	0.90	0.84	0.74	0.90	0.59	0.81	41
Australia_University of Western Australia	0.77	0.98	0.83	0.99	0.77	0.97	0.83	0.89	0.80	0.88	0.91	19
USA_State University of New York, Binghamton	0.51	0.43	0.47	0.42	0.40	0.50	0.48	0.49	0.71	0.47	0.51	64
Canada_University of Waterloo	0.86	0.77	0.63	0.85	0.84	0.90	0.89	0.82	0.69	0.68	0.21	133
Russia_Kozma Minin Nizhny Novgorod State Pedagogical University	0.00	0.04	0.02	0.07	0.00	0.05	0.08	0.08	0.07	0.14	0.01	270
Netherlands_University of Groningen	0.81	0.98	0.86	0.98	0.83	0.78	0.83	0.81	0.80	0.96	0.22	116
Iraq_University of Samarra	0.00	0.02	0.09	0.02	0.00	0.00	0.08	0.00	0.03	0.02	0.01	279
Portugal_ISCTE – University Institute of Lisbon	0.13	0.26	0.29	0.35	0.20	0.39	0.35	0.49	0.20	0.43	0.08	209
Chile_Pontificial Catholic University of Valparaiso	0.24	0.24	0.20	0.29	0.20	0.52	0.28	0.40	0.34	0.33	0.32	81
Russia_Belgorod State Technological University	0.19	0.03	0.02	0.04	0.15	0.30	0.08	0.21	0.20	0.33	0.16	168
Taiwan_Tamkang University	0.33	0.24	0.16	0.26	0.31	0.42	0.30	0.33	0.26	0.31	0.30	82
Canada_University of Ottawa	0.75	0.87	0.77	0.90	0.68	0.85	0.82	0.76	0.75	0.78	0.82	38
USA_Texas A&M University	0.92	0.70	0.59	0.75	0.92	0.77	0.94	0.67	0.87	0.84	0.83	37
Canada_Queens University	0.65	0.78	0.57	0.86	0.64	0.78	0.77	0.69	0.86	0.80	0.19	150
Germany_Karlsruhe Institute of Technology	0.86	0.84	0.76	0.83	0.88	0.64	0.90	0.81	0.89	0.91	0.22	123
USA_University of Houston	0.61	0.58	0.57	0.61	0.61	0.32	0.72	0.50	0.73	0.54	0.15	171
South Africa_Stellenbosch University	0.63	0.63	0.58	0.73	0.57	0.57	0.62	0.59	0.80	0.70	0.17	166
South Africa_University of Witwatersrand	0.68	0.73	0.69	0.77	0.68	0.93	0.72	0.75	0.90	0.94	0.20	138
USA_Georgia Institute of Technology	0.96	0.74	0.90	0.63	0.96	0.88	0.97	0.85	0.93	0.92	0.91	18
Egypt_Alexandria University	0.40	0.14	0.20	0.14	0.20	0.15	0.35	0.39	0.14	0.50	0.27	85
USA_University of California, Santa Barbara	0.92	0.97	0.97	0.89	0.93	0.81	0.94	0.77	0.94	0.90	0.94	14
Greece_University of Patras	0.24	0.34	0.35	0.32	0.20	0.09	0.08	0.24	0.15	0.23	0.23	102
South Africa_University of KwaZulu Natal	0.36	0.64	0.58	0.63	0.31	0.69	0.48	0.54	0.68	0.65	0.58	61
Italy_Ca`Foscari University of Venice	0.40	0.31	0.40	0.33	0.31	0.63	0.28	0.49	0.38	0.38	0.10	193
Iraq_Al-Farabi University College	0.00	0.00	0.00	0.00	0.00	0.00	0.08	0.00	0.29	0.17	0.01	272
Canada_McMaster University	0.83	0.99	0.85	0.99	0.83	0.94	0.89	0.82	0.91	0.96	0.23	100
Belgium_Vrije Universiteit Brussels (VUB)	0.64	0.94	0.68	0.96	0.71	0.63	0.73	0.78	0.86	0.93	0.20	136
Germany_University of Gottingen	0.86	0.92	0.85	0.91	0.83	0.58	0.86	0.71	0.86	0.90	0.21	126
Australia_University of Adelaide	0.73	0.97	0.95	0.96	0.76	0.95	0.83	0.86	0.84	0.84	0.90	22
Iraq_Southern Technical University	0.00	0.04	0.11	0.02	0.00	0.00	0.08	0.26	0.04	0.02	0.06	220
Iraq_Madenat Al-elem University College	0.00	0.02	0.08	0.02	0.00	0.31	0.08	0.08	0.04	0.05	0.07	214
Australia_Monash University	0.91	0.94	0.82	0.95	0.91	0.83	0.94	0.87	0.88	0.76	0.91	17
Iraq_Baghdad College Of Economic Sciences University	0.00	0.04	0.03	0.04	0.00	0.00	0.08	0.16	0.17	0.01	0.05	225
Thailand_Mahasarakham University	0.00	0.12	0.12	0.10	0.00	0.38	0.08	0.23	0.08	0.05	0.03	246
Canada_York University	0.67	0.57	0.60	0.61	0.74	0.78	0.82	0.77	0.73	0.55	0.18	159
Australia_University of Queensland Australia	0.90	0.97	0.82	0.97	0.90	0.89	0.92	0.88	0.89	0.83	0.23	104
Australia_University of New South Wales	0.88	0.93	0.77	0.96	0.90	0.96	0.92	0.91	0.90	0.81	0.23	105
Belgium_Katholieke Universiteit Leuven (KU Leuven)	0.92	0.95	0.77	0.95	0.92	0.66	0.92	0.81	0.87	0.89	0.22	115
Germany_University of Cologne	0.61	0.75	0.70	0.74	0.60	0.51	0.68	0.66	0.89	0.75	0.71	52
Vietnam_Can Tho University	0.00	0.13	0.27	0.11	0.00	0.00	0.08	0.26	0.05	0.14	0.11	190
Belgium_University Catholique de Louvain	0.80	0.96	0.89	0.95	0.78	0.73	0.80	0.83	0.85	0.96	0.89	26
Iraq_Al-Kunooze University College	0.00	0.00	0.00	0.00	0.00	0.21	0.08	0.05	0.01	0.02	0.04	238
Australia_Queensland University of Technology	0.74	0.79	0.69	0.86	0.69	0.94	0.79	0.79	0.81	0.79	0.82	39
Germany_University of Freiburg	0.79	0.98	0.74	0.98	0.74	0.69	0.79	0.78	0.91	0.98	0.22	121
Greece_Athens University of Economics and Business	0.19	0.29	0.28	0.38	0.20	0.12	0.21	0.35	0.20	0.60	0.07	213
Germany_Technical University of Munich	0.93	0.99	0.74	0.99	0.93	0.64	0.94	0.82	0.97	0.98	0.23	106
Germany_University of Hamburg	0.72	0.91	0.82	0.91	0.73	0.54	0.75	0.66	0.96	0.80	0.20	139
Germany_Technical University of Berlin	0.88	0.88	0.58	0.95	0.87	0.55	0.88	0.75	0.96	0.94	0.21	127

Comparing Partial Rankings to the Adequate Part of the Original Ranking

The final step is to compare the results of the partial rankings to the corresponding part of the original rankings. The results of the Spearman’s rank correlation shows a strong positive relationship between the two ranking.

cor(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## [1] 0.7588123

cor.test(B$Rank,RANK_RUR[rownames(B),],method="spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  B$Rank and RANK_RUR[rownames(B), ]
## S = 882414, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.7588123

Summary of Findings about League B

The middle league B satisfies all three criteria, i.e. it is significant, stable and has high correlation with the original ranking.

Specifying Overlaps

Bicluster might (or might not) overlap. Analyzing the overlaps can give a subtler picture of HEIs and indicators.

Venn Diagram of Indicators

Fig. 39 shows the Venn diagram of the indicators. The red circle contains those indicators that are in the upper league (League A), in the the blue circle those indicators can be found that are in the lower league (League C). The green circle indicates the middle league’s (League B) indicators.

T<-biclust::bicluster(orig_mtx,res,number = 1)
League_A<-T[[1]]
R<-biclust::bicluster(orig_mtx,rres,number = 1)
League_C<-R[[1]]
B<-biclust::bicluster(orig_mtx,bres,number = 1)
League_B<-B[[1]]
draw.triple.venn(area1=nrow(as.matrix(colnames(League_A))),area2=nrow(as.matrix(colnames(League_B))),area3=nrow(as.matrix(colnames(League_C))),n12=nrow(as.matrix(intersect(colnames(League_A),colnames(League_B)))),n13=nrow(as.matrix(intersect(colnames(League_A),colnames(League_C)))),n23=nrow(as.matrix(intersect(colnames(League_B),colnames(League_C)))),n123=nrow(as.matrix(intersect(intersect(colnames(League_A),colnames(League_B)),colnames(League_C)))),fill=c("red","green","blue"),category=c("League A","League B","League C"),main="Venn Diagram of indicators")

Fig. 39 Venn diagram of the indicators

## (polygon[GRID.polygon.27], polygon[GRID.polygon.28], polygon[GRID.polygon.29], polygon[GRID.polygon.30], polygon[GRID.polygon.31], polygon[GRID.polygon.32], text[GRID.text.33], text[GRID.text.34], text[GRID.text.35], text[GRID.text.36], text[GRID.text.37], text[GRID.text.38], text[GRID.text.39])

One interesting finding is, that all of the indicators in the middle league are part of the lower league’s indicators.

##Venn Diagram of HEIs

Fig. 40 shows the Venn diagram of the HEIs. The red circle contains those HEIs that are in the upper league (League A), in the the blue circle those HEIs can be found that are in the lower league (League C). The green circle indicates the middle league’s (League B) HEIs.

draw.triple.venn(area1=nrow(as.matrix(rownames(League_A))),area2=nrow(as.matrix(rownames(League_B))),area3=nrow(as.matrix(rownames(League_C))),n12=nrow(as.matrix(intersect(rownames(League_A),rownames(League_B)))),n13=nrow(as.matrix(intersect(rownames(League_A),rownames(League_C)))),n23=nrow(as.matrix(intersect(rownames(League_B),rownames(League_C)))),n123=nrow(as.matrix(intersect(intersect(rownames(League_A),rownames(League_B)),rownames(League_C)))),fill=c("red","green","blue"),category=c("League A","League B","League C"),main="Venn Diagram of HEIs")

Fig. 40 Venn diagram of the HEIs

## (polygon[GRID.polygon.40], polygon[GRID.polygon.41], polygon[GRID.polygon.42], polygon[GRID.polygon.43], polygon[GRID.polygon.44], polygon[GRID.polygon.45], text[GRID.text.46], text[GRID.text.47], text[GRID.text.48], text[GRID.text.49], text[GRID.text.50], text[GRID.text.51], text[GRID.text.52], text[GRID.text.53], text[GRID.text.54], text[GRID.text.55])

Seven HEIs are in all of the three leagues. There are 11 HEIs which belong only to the upper league, and there are 18 HEIs which are just in the lower league.

Summing Up the Conclusions

The above proposed biclustering method can help to identify which HEIs can be compared based on which indicators in university rankings. With the iBBiG method the upper and lower league(s) (League(s) A and League(s) C) can be determined and the BicARE method can specify the middle league(s) (League(s) B).