1 FRESA.CAD Sonar Benchmark

##Sonar, Mines vs. Rocks Data Set

op <- par(no.readonly = TRUE)

data(Sonar)
Sonar$Class <- 1*(Sonar$Class == "M")
#Sonar.mat <- as.data.frame(model.matrix(Class~.*.,Sonar))
Sonar.mat <- as.data.frame(model.matrix(Class~.,Sonar))
Sonar.mat$`(Intercept)` <- NULL
Sonar.mat$Class <- as.numeric(Sonar$Class)

fnames <- colnames(Sonar.mat)
fnames <- str_replace_all(fnames," ","_")
fnames <- str_replace_all(fnames,"/","_")
fnames <- str_replace_all(fnames,":",".")
colnames(Sonar.mat) <- fnames

ExperimentName <- "Sonar"
bswimsReps <- 20;
theData <- Sonar.mat;
theOutcome <- "Class";
reps <- 120;
fraction <- 0.75;

BSIWIMSFileName <- paste(ExperimentName,"FRESAMethod.RDATA",sep = "_")
CVFileName <- paste(ExperimentName,"CVMethod.RDATA",sep = "_")

1.1 Benchmarking



BSWiMSMODEL <- BSWiMS.model(formula = paste(theOutcome," ~ 1"),data = theData,NumberofRepeats = bswimsReps)

save(BSWiMSMODEL,file = BSIWIMSFileName)

par(mfrow = c(2,2),cex = 0.6);
cp <- BinaryBenchmark(theData,theOutcome,reps,fraction)

par(op );

save(cp,file = CVFileName)
load(CVFileName)

1.2 Results

1.2.1 Classifier Results


hm <- heatMaps(Outcome = "Outcome",data = cp$testPredictions,title = "Heat Map",Scale = TRUE,hCluster = "col",cexRow = 0.25,cexCol = 0.75,srtCol = 45) 


#The Times
pander::pander(cp$cpuElapsedTimes)
BSWiMS RF RPART LASSO SVM KNN ENS
1.979 0.1221 0.01117 0.842 0.009167 0.01158 2.964 
learningTime <- -1*cp$cpuElapsedTimes
pr <- plot(cp)

1.2.2 Radar Plots

op <- par(no.readonly = TRUE)

library(fmsb)
par(mfrow = c(1,2),xpd = TRUE,pty = "s",mar = c(1,1,1,1))

mNames <- names(cp$cpuElapsedTimes)

classRanks <- c(pr$minMaxMetrics$BER[1],pr$minMaxMetrics$ACC[2],pr$minMaxMetrics$AUC[2],pr$minMaxMetrics$SEN[2],pr$minMaxMetrics$SPE[2],min(cp$cpuElapsedTimes))
classRanks <- rbind(classRanks,c(pr$minMaxMetrics$BER[2],0,0,0,0,max(cp$cpuElapsedTimes)))
classRanks <- as.data.frame(rbind(classRanks,cbind(t(pr$metrics[c("BER","ACC","AUC","SEN","SPE"),mNames]),cp$cpuElapsedTimes)))
colnames(classRanks) <- c("BER","ACC","AUC","SEN","SPE","CPU")

classRanks$BER <- -classRanks$BER
classRanks$CPU <- -classRanks$CPU

colors_border = c( rgb(1.0,0.0,0.0,1.0), rgb(0.0,1.0,0.0,1.0) , rgb(0.0,0.0,1.0,1.0), rgb(0.2,0.2,0.0,1.0), rgb(0.0,1.0,1.0,1.0), rgb(1.0,0.0,1.0,1.0), rgb(0.0,0.0,0.0,1.0) )
colors_in = c( rgb(1.0,0.0,0.0,0.05), rgb(0.0,1.0,0.0,0.05) , rgb(0.0,0.0,1.0,0.05),rgb(1.0,1.0,0.0,0.05), rgb(0.0,1.0,1.0,0.05) , rgb(1.0,0.0,1.0,0.05), rgb(0.0,0.0,0.0,0.05) )
radarchart(classRanks,axistype = 0,maxmin = T,pcol = colors_border,pfcol = colors_in,plwd = c(6,2,2,2,2,2,2),plty = 1, cglcol = "grey", cglty = 1,axislabcol = "black",cglwd = 0.8, vlcex  = 0.5 ,title = "Prediction Model")

legend("topleft",legend = rownames(classRanks[-c(1,2),]),bty = "n",pch = 20,col = colors_in,text.col = colors_border,cex = 0.5,pt.cex = 2)


filnames <- c("BSWiMS","LASSO_MIN","RF","IDI","tStudent","kendall","mRMR.classic")

filterRanks <- c(pr$minMaxMetrics$BER[1],pr$minMaxMetrics$ACC[2],pr$minMaxMetrics$AUC[2],pr$minMaxMetrics$SEN[2],pr$minMaxMetrics$SPE[2],max(cp$jaccard),min(cp$featsize));

filterRanks <- rbind(filterRanks,c(pr$minMaxMetrics$BER[2],0,0,0,0,min(cp$jaccard),max(cp$featsize)));

filterRanks <- as.data.frame(rbind(filterRanks,cbind(t(pr$metrics_filter[c("BER","ACC","AUC","SEN","SPE"),filnames]),cp$jaccard[filnames],cp$featsize[filnames])));
colnames(filterRanks) <- c("BER","ACC","AUC","SEN","SPE","Jaccard","SIZE")
filterRanks$BER <- -filterRanks$BER
filterRanks$SIZE <- -filterRanks$SIZE

colors_border = c( rgb(1.0,0.0,0.0,1.0), rgb(0.0,1.0,0.0,1.0) , rgb(0.0,0.0,1.0,1.0), rgb(0.2,0.2,0.0,1.0), rgb(0.0,1.0,1.0,1.0), rgb(1.0,0.0,1.0,1.0), rgb(0.0,0.0,0.0,1.0) )
colors_in = c( rgb(1.0,0.0,0.0,0.05), rgb(0.0,1.0,0.0,0.05) , rgb(0.0,0.0,1.0,0.05),rgb(1.0,1.0,0.0,0.05), rgb(0.0,1.0,1.0,0.05) , rgb(1.0,0.0,1.0,0.05), rgb(0.0,0.0,0.0,0.05) )
radarchart(filterRanks,axistype = 0,maxmin = T,pcol = colors_border,pfcol = colors_in,plwd = c(6,2,2,2,2,2,2),plty = 1, cglcol = "grey", cglty = 1,axislabcol = "black",cglwd = 0.8, vlcex  = 0.6,title = "Filter Method" )


legend("topleft",legend = rownames(filterRanks[-c(1,2),]),bty = "n",pch = 20,col = colors_in,text.col = colors_border,cex = 0.5,pt.cex = 2)


detach("package:fmsb", unload=TRUE)

par(mfrow = c(1,1))
par(op)

1.2.3 Feature Analysis



rm <- rowMeans(cp$featureSelectionFrequency)
selFrequency <- cp$featureSelectionFrequency[rm > 0.1,]
gplots::heatmap.2(as.matrix(selFrequency),trace = "none",mar = c(10,10),main = "Features",cexRow = 0.25,cexCol = 0.5)



topFeat <- min(ncol(BSWiMSMODEL$bagging$formulaNetwork),30);
gplots::heatmap.2(BSWiMSMODEL$bagging$formulaNetwork[1:topFeat,1:topFeat],trace="none",mar = c(10,10),main = "B:SWiMS Formula Network",cexRow = 0.5,cexCol = 0.5)

pander::pander(summary(BSWiMSMODEL$bagging$bagged.model,caption="Colon",round = 3))

  • coefficients:

    Table continues below
      Estimate lower OR upper u.Accuracy r.Accuracy
    V11 1.516 2.697 4.553 7.688 0.7452 0.7187
    V45 1.658 2.841 5.249 9.696 0.6394 0.7392
    V49 4.972 19.54 144.3 1066 0.6827 0.7281
    V37 -0.8486 0.3023 0.428 0.606 0.6346 0.712
    V12 1.194 2.005 3.302 5.436 0.7404 0.7132
    V36 -0.6306 0.4067 0.5323 0.6967 0.6587 0.73
    V47 1.634 2.511 5.123 10.45 0.6202 0.727
    V46 0.7694 1.535 2.158 3.035 0.6106 0.7198
    V48 3.132 5.573 22.92 94.24 0.6875 0.7269
    V10 1.178 1.824 3.249 5.786 0.6971 0.7202
    V20 0.1839 1.099 1.202 1.315 0.6394 0.6841
    V35 -0.5254 0.4565 0.5913 0.7661 0.5865 0.7127
    V44 0.5503 1.31 1.734 2.295 0.5913 0.7078
    V4 3.65 5.812 38.49 255 0.6058 0.7385
    V9 1.068 1.675 2.909 5.053 0.6923 0.7
    V13 0.9644 1.581 2.623 4.352 0.6683 0.704
    V21 0.4517 1.229 1.571 2.009 0.6298 0.7104
    V22 0.3246 1.151 1.383 1.663 0.5865 0.7101
    V43 0.1341 1.057 1.144 1.237 0.5865 0.6747
    V1 1.933 2.204 6.91 21.67 0.601 0.7005
    V14 -0.3944 0.5294 0.6741 0.8582 0.5962 0.742
    V28 0.2202 1.083 1.246 1.434 0.5144 0.7073
    V51 4.672 5.118 106.9 2234 0.6683 0.7025
    V34 -0.06093 0.9047 0.9409 0.9785 0.5865 0.6811
    V52 7.683 14.06 2172 335383 0.6394 0.729
    Table continues below
      full.Accuracy u.AUC r.AUC full.AUC IDI NRI
    V11 0.782 0.7418 0.7162 0.7817 0.1263 0.7231
    V45 0.7745 0.6446 0.7377 0.7744 0.1219 0.7548
    V49 0.7606 0.6832 0.7264 0.7583 0.1079 0.8228
    V37 0.7635 0.6258 0.7126 0.7622 0.09691 0.616
    V12 0.7603 0.736 0.712 0.7581 0.09952 0.8158
    V36 0.782 0.6516 0.728 0.7817 0.08792 0.5747
    V47 0.7511 0.6201 0.7241 0.7492 0.08936 0.5684
    V46 0.7456 0.6124 0.7164 0.7435 0.08846 0.6466
    V48 0.7632 0.6877 0.724 0.7612 0.08286 0.6913
    V10 0.7635 0.6961 0.7187 0.7619 0.06302 0.7082
    V20 0.7184 0.6362 0.6841 0.7161 0.07619 0.646
    V35 0.7466 0.5775 0.7139 0.7445 0.0669 0.3521
    V44 0.7382 0.5924 0.7056 0.7372 0.06744 0.577
    V4 0.7649 0.6053 0.7363 0.7637 0.0543 0.5115
    V9 0.7454 0.6929 0.697 0.7433 0.06077 0.5509
    V13 0.7512 0.6658 0.7014 0.7493 0.06036 0.5833
    V21 0.7579 0.6239 0.708 0.7556 0.05837 0.652
    V22 0.7574 0.5782 0.7083 0.7553 0.05438 0.4785
    V43 0.7131 0.5834 0.6729 0.7117 0.0506 0.538
    V1 0.7335 0.6027 0.6977 0.7321 0.04787 0.329
    V14 0.7756 0.5885 0.7388 0.7733 0.04283 0.4263
    V28 0.7446 0.4956 0.7053 0.7428 0.04334 0.4918
    V51 0.7326 0.6664 0.7014 0.7311 0.04252 0.4976
    V34 0.7196 0.5769 0.6808 0.7186 0.04254 0.3909
    V52 0.7469 0.6394 0.7266 0.7453 0.04292 0.4801
      z.IDI z.NRI Frequency
    V11 5.625 5.628 1
    V45 5.244 6.102 1
    V49 4.852 6.67 1
    V37 4.76 4.682 1
    V12 4.683 6.438 1
    V36 4.556 4.323 1
    V47 4.475 4.477 0.9
    V46 4.39 5.049 0.55
    V48 4.249 5.367 1
    V10 3.975 5.531 1
    V20 3.971 4.928 0.35
    V35 3.925 2.59 1
    V44 3.804 4.441 0.45
    V4 3.766 3.914 1
    V9 3.74 4.255 1
    V13 3.645 4.445 0.8
    V21 3.566 4.964 0.85
    V22 3.428 3.559 0.65
    V43 3.314 4.049 0.15
    V1 3.275 2.463 0.35
    V14 3.198 3.144 0.3
    V28 3.066 3.685 0.4
    V51 3 3.746 0.4
    V34 2.986 2.891 0.15
    V52 2.952 3.636 0.55
  • Accuracy: 0.8077
  • tAUC: 0.8062
  • sensitivity: 0.8288
  • specificity: 0.7835

  • bootstrap:



hm <- heatMaps(Outcome = theOutcome,data = theData[,c(theOutcome,rownames(selFrequency))],title = "Heat Map",Scale = TRUE,hCluster = "col",cexRow = 0.25,cexCol = 0.5,srtCol = 45)


vlist <- rownames(selFrequency)
vlist <- cbind(vlist,vlist)
univ <- univariateRankVariables(variableList = vlist,formula = paste(theOutcome,"~1"),Outcome = theOutcome,data = theData,type = "LOGIT",rankingTest = "zIDI",uniType = "Binary")[,c("controlMean","controlStd","caseMean","caseStd","ROCAUC","WilcoxRes.p")] 

cnames <- colnames(univ);
univ <- cbind(univ,rm[rownames(univ)])
colnames(univ) <- c(cnames,"Frequency")
univ <- univ[order(-univ[,5]),]
pander::pander(univ[1:topFeat,],caption = "Features",round = 4)
Features (continued below)
  controlMean controlStd caseMean caseStd ROCAUC WilcoxRes.p
V11 0.1747 0.1134 0.2896 0.1254 0.7811 0
V12 0.1916 0.1347 0.3015 0.1241 0.7429 0
V10 0.1593 0.1132 0.251 0.1374 0.7327 0
V49 0.0384 0.0304 0.0637 0.0364 0.7313 0
V9 0.1374 0.0999 0.2135 0.1222 0.7308 0
V48 0.0695 0.0482 0.1106 0.0671 0.7063 0
V13 0.2262 0.1381 0.3144 0.1307 0.7047 0
V51 0.0123 0.0086 0.0194 0.0135 0.6994 0
V47 0.0945 0.0678 0.1469 0.0945 0.6974 0
V52 0.0105 0.0071 0.016 0.0108 0.688 0
V46 0.1169 0.0938 0.1988 0.1514 0.6871 0
V45 0.1423 0.0957 0.2452 0.1741 0.6727 0
V4 0.0414 0.0312 0.0648 0.0545 0.6652 0
V36 0.4607 0.2623 0.3186 0.2484 0.6652 0
V5 0.062 0.0472 0.0867 0.0598 0.6537 2e-04
V1 0.0225 0.0147 0.035 0.0271 0.6523 1e-04
V44 0.1751 0.1074 0.2481 0.1444 0.6511 1e-04
V21 0.5423 0.2488 0.6674 0.2524 0.6445 1e-04
V35 0.4555 0.2612 0.3376 0.2455 0.6415 6e-04
V8 0.1176 0.0798 0.1498 0.0872 0.641 8e-04
V43 0.2118 0.1303 0.2769 0.1398 0.6409 2e-04
V37 0.4173 0.243 0.317 0.2281 0.6281 6e-04
V6 0.0962 0.065 0.1119 0.0526 0.6246 0.0018
V20 0.5002 0.2594 0.6179 0.2541 0.6236 9e-04
V2 0.0303 0.024 0.0455 0.0378 0.6228 0.0015
V50 0.0178 0.0126 0.0227 0.0142 0.6218 0.003
  Frequency
V11 0.9975
V12 0.9725
V10 0.8
V49 0.9017
V9 0.8258
V48 0.7917
V13 0.78
V51 0.8158
V47 0.775
V52 0.8467
V46 0.7625
V45 0.8575
V4 0.8608
V36 0.9367
V5 0.74
V1 0.8217
V44 0.8058
V21 0.85
V35 0.7317
V8 0.6975
V43 0.6908
V37 0.7825
V6 0.6217
V20 0.7292
V2 0.6675
V50 0.6233

1.2.4 Feature Analysis



rm <- rowMeans(cp$featureSelectionFrequency)
selFrequency <- cp$featureSelectionFrequency[rm > 0.1,]
gplots::heatmap.2(as.matrix(selFrequency),trace = "none",mar = c(10,10),main = "Features",cexRow = 0.25,cexCol = 0.5)



topFeat <- min(ncol(BSWiMSMODEL$bagging$formulaNetwork),30);
gplots::heatmap.2(BSWiMSMODEL$bagging$formulaNetwork[1:topFeat,1:topFeat],trace="none",mar = c(10,10),main = "B:SWiMS Formula Network",cexRow = 0.5,cexCol = 0.5)

pander::pander(summary(BSWiMSMODEL$bagging$bagged.model,caption="Colon",round = 3))

  • coefficients:

    Table continues below
      Estimate lower OR upper u.Accuracy r.Accuracy
    V11 1.516 2.697 4.553 7.688 0.7452 0.7187
    V45 1.658 2.841 5.249 9.696 0.6394 0.7392
    V49 4.972 19.54 144.3 1066 0.6827 0.7281
    V37 -0.8486 0.3023 0.428 0.606 0.6346 0.712
    V12 1.194 2.005 3.302 5.436 0.7404 0.7132
    V36 -0.6306 0.4067 0.5323 0.6967 0.6587 0.73
    V47 1.634 2.511 5.123 10.45 0.6202 0.727
    V46 0.7694 1.535 2.158 3.035 0.6106 0.7198
    V48 3.132 5.573 22.92 94.24 0.6875 0.7269
    V10 1.178 1.824 3.249 5.786 0.6971 0.7202
    V20 0.1839 1.099 1.202 1.315 0.6394 0.6841
    V35 -0.5254 0.4565 0.5913 0.7661 0.5865 0.7127
    V44 0.5503 1.31 1.734 2.295 0.5913 0.7078
    V4 3.65 5.812 38.49 255 0.6058 0.7385
    V9 1.068 1.675 2.909 5.053 0.6923 0.7
    V13 0.9644 1.581 2.623 4.352 0.6683 0.704
    V21 0.4517 1.229 1.571 2.009 0.6298 0.7104
    V22 0.3246 1.151 1.383 1.663 0.5865 0.7101
    V43 0.1341 1.057 1.144 1.237 0.5865 0.6747
    V1 1.933 2.204 6.91 21.67 0.601 0.7005
    V14 -0.3944 0.5294 0.6741 0.8582 0.5962 0.742
    V28 0.2202 1.083 1.246 1.434 0.5144 0.7073
    V51 4.672 5.118 106.9 2234 0.6683 0.7025
    V34 -0.06093 0.9047 0.9409 0.9785 0.5865 0.6811
    V52 7.683 14.06 2172 335383 0.6394 0.729
    Table continues below
      full.Accuracy u.AUC r.AUC full.AUC IDI NRI
    V11 0.782 0.7418 0.7162 0.7817 0.1263 0.7231
    V45 0.7745 0.6446 0.7377 0.7744 0.1219 0.7548
    V49 0.7606 0.6832 0.7264 0.7583 0.1079 0.8228
    V37 0.7635 0.6258 0.7126 0.7622 0.09691 0.616
    V12 0.7603 0.736 0.712 0.7581 0.09952 0.8158
    V36 0.782 0.6516 0.728 0.7817 0.08792 0.5747
    V47 0.7511 0.6201 0.7241 0.7492 0.08936 0.5684
    V46 0.7456 0.6124 0.7164 0.7435 0.08846 0.6466
    V48 0.7632 0.6877 0.724 0.7612 0.08286 0.6913
    V10 0.7635 0.6961 0.7187 0.7619 0.06302 0.7082
    V20 0.7184 0.6362 0.6841 0.7161 0.07619 0.646
    V35 0.7466 0.5775 0.7139 0.7445 0.0669 0.3521
    V44 0.7382 0.5924 0.7056 0.7372 0.06744 0.577
    V4 0.7649 0.6053 0.7363 0.7637 0.0543 0.5115
    V9 0.7454 0.6929 0.697 0.7433 0.06077 0.5509
    V13 0.7512 0.6658 0.7014 0.7493 0.06036 0.5833
    V21 0.7579 0.6239 0.708 0.7556 0.05837 0.652
    V22 0.7574 0.5782 0.7083 0.7553 0.05438 0.4785
    V43 0.7131 0.5834 0.6729 0.7117 0.0506 0.538
    V1 0.7335 0.6027 0.6977 0.7321 0.04787 0.329
    V14 0.7756 0.5885 0.7388 0.7733 0.04283 0.4263
    V28 0.7446 0.4956 0.7053 0.7428 0.04334 0.4918
    V51 0.7326 0.6664 0.7014 0.7311 0.04252 0.4976
    V34 0.7196 0.5769 0.6808 0.7186 0.04254 0.3909
    V52 0.7469 0.6394 0.7266 0.7453 0.04292 0.4801
      z.IDI z.NRI Frequency
    V11 5.625 5.628 1
    V45 5.244 6.102 1
    V49 4.852 6.67 1
    V37 4.76 4.682 1
    V12 4.683 6.438 1
    V36 4.556 4.323 1
    V47 4.475 4.477 0.9
    V46 4.39 5.049 0.55
    V48 4.249 5.367 1
    V10 3.975 5.531 1
    V20 3.971 4.928 0.35
    V35 3.925 2.59 1
    V44 3.804 4.441 0.45
    V4 3.766 3.914 1
    V9 3.74 4.255 1
    V13 3.645 4.445 0.8
    V21 3.566 4.964 0.85
    V22 3.428 3.559 0.65
    V43 3.314 4.049 0.15
    V1 3.275 2.463 0.35
    V14 3.198 3.144 0.3
    V28 3.066 3.685 0.4
    V51 3 3.746 0.4
    V34 2.986 2.891 0.15
    V52 2.952 3.636 0.55
  • Accuracy: 0.8077
  • tAUC: 0.8062
  • sensitivity: 0.8288
  • specificity: 0.7835

  • bootstrap:



hm <- heatMaps(Outcome = theOutcome,data = theData[,c(theOutcome,rownames(selFrequency))],title = "Heat Map",Scale = TRUE,hCluster = "col",cexRow = 0.25,cexCol = 0.5,srtCol = 45)


vlist <- rownames(selFrequency)
vlist <- cbind(vlist,vlist)
univ <- univariateRankVariables(variableList = vlist,formula = paste(theOutcome,"~1"),Outcome = theOutcome,data = theData,type = "LOGIT",rankingTest = "zIDI",uniType = "Binary")[,c("controlMean","controlStd","caseMean","caseStd","ROCAUC","WilcoxRes.p")] 

cnames <- colnames(univ);
univ <- cbind(univ,rm[rownames(univ)])
colnames(univ) <- c(cnames,"Frequency")
univ <- univ[order(-univ[,5]),]
pander::pander(univ[1:topFeat,],caption = "Features",round = 4)
Features (continued below)
  controlMean controlStd caseMean caseStd ROCAUC WilcoxRes.p
V11 0.1747 0.1134 0.2896 0.1254 0.7811 0
V12 0.1916 0.1347 0.3015 0.1241 0.7429 0
V10 0.1593 0.1132 0.251 0.1374 0.7327 0
V49 0.0384 0.0304 0.0637 0.0364 0.7313 0
V9 0.1374 0.0999 0.2135 0.1222 0.7308 0
V48 0.0695 0.0482 0.1106 0.0671 0.7063 0
V13 0.2262 0.1381 0.3144 0.1307 0.7047 0
V51 0.0123 0.0086 0.0194 0.0135 0.6994 0
V47 0.0945 0.0678 0.1469 0.0945 0.6974 0
V52 0.0105 0.0071 0.016 0.0108 0.688 0
V46 0.1169 0.0938 0.1988 0.1514 0.6871 0
V45 0.1423 0.0957 0.2452 0.1741 0.6727 0
V4 0.0414 0.0312 0.0648 0.0545 0.6652 0
V36 0.4607 0.2623 0.3186 0.2484 0.6652 0
V5 0.062 0.0472 0.0867 0.0598 0.6537 2e-04
V1 0.0225 0.0147 0.035 0.0271 0.6523 1e-04
V44 0.1751 0.1074 0.2481 0.1444 0.6511 1e-04
V21 0.5423 0.2488 0.6674 0.2524 0.6445 1e-04
V35 0.4555 0.2612 0.3376 0.2455 0.6415 6e-04
V8 0.1176 0.0798 0.1498 0.0872 0.641 8e-04
V43 0.2118 0.1303 0.2769 0.1398 0.6409 2e-04
V37 0.4173 0.243 0.317 0.2281 0.6281 6e-04
V6 0.0962 0.065 0.1119 0.0526 0.6246 0.0018
V20 0.5002 0.2594 0.6179 0.2541 0.6236 9e-04
V2 0.0303 0.024 0.0455 0.0378 0.6228 0.0015
V50 0.0178 0.0126 0.0227 0.0142 0.6218 0.003
  Frequency
V11 0.9975
V12 0.9725
V10 0.8
V49 0.9017
V9 0.8258
V48 0.7917
V13 0.78
V51 0.8158
V47 0.775
V52 0.8467
V46 0.7625
V45 0.8575
V4 0.8608
V36 0.9367
V5 0.74
V1 0.8217
V44 0.8058
V21 0.85
V35 0.7317
V8 0.6975
V43 0.6908
V37 0.7825
V6 0.6217
V20 0.7292
V2 0.6675
V50 0.6233