Sonar Prediction in R¶

# Sonar

# Binary classification, numeric inputs

# Dataset: https://archive.ics.uci.edu/ml/datasets/Connectionist+Bench+(Sonar,+Mines+vs.+Rocks)
# World-class results: http://www.is.umk.pl/projects/datasets.html#Sonar

library(mlbench)
library(caret)
library(doMC)
library(caretEnsemble)

# use multiple cores
registerDoMC(cores=8)

# 1. Load the dataset
data(Sonar)
dataset <- Sonar

# 2. Summarize data
# dimensions of dataaset
dim(dataset)
# split input and output
x <- dataset[,1:60]
y <- dataset[,61]
# class distribution
cbind(freq=table(y), percentage=prop.table(table(y))*100)
# summarize attribute distributions
summary(dataset)
# summarize correlations between input variables
cor(x)

# 3. Visualize Data
# box and whisker plots for each attribute
scales <- list(x=list(relation="free"), y=list(relation="free"))
featurePlot(x=x, y=y, plot="box", scales=scales)
# density plots for each attribute by class value
featurePlot(x=x, y=y, plot="density", scales=scales)

# 4 Data Transforms
dataset[,1:60] <- scale(dataset[,1:60])

# 5. Evaluate Algorithms
# Run algorithms using 10-fold cross validation
control <- trainControl(method="repeatedcv", number=10, repeats=3)
# GLM
set.seed(7)
fit.glm <- train(Class~., data=dataset, method="glm", metric="Accuracy", trControl=control)
# LDA
set.seed(7)
fit.lda <- train(Class~., data=dataset, method="lda", metric="Accuracy", trControl=control)
# SVM
set.seed(7)
grid <- expand.grid(.sigma=c(0.01,0.05,0.1), .C=c(1))
fit.svm <- train(Class~., data=dataset, method="svmRadial", metric="Accuracy", tuneGrid=grid, trControl=control)
# CART
set.seed(7)
grid <- expand.grid(.cp=c(0.01,0.05,0.1))
fit.cart <- train(Class~., data=dataset, method="rpart", metric="Accuracy", tuneGrid=grid, trControl=control)
# kNN
set.seed(7)
grid <- expand.grid(.k=c(1,3,5,7))
fit.knn <- train(Class~., data=dataset, method="knn", metric="Accuracy", tuneGrid=grid, trControl=control)
# Compare algorithms
results <- resamples(list(SVM=fit.svm, CART=fit.cart, kNN=fit.knn, glm=fit.glm, lda=fit.lda))
summary(results)
dotplot(results)

# 6. Improve Results
# ensemble
control <- trainControl(method="repeatedcv", number=10, repeats=3, savePredictions=TRUE, classProbs=TRUE)
models <- caretList(Class~., data=dataset, trControl=control, metric='Accuracy', methodList=c('glm', 'lda'),
  tuneList=list(
    svmRadial=caretModelSpec(method='svmRadial', tuneGrid=expand.grid(.sigma=c(0.05), .C=c(1))),
    rpart=caretModelSpec(method='rpart', tuneGrid=expand.grid(.cp=c(0.1))),
    knn=caretModelSpec(method='knn', tuneGrid=expand.grid(.k=c(1)))
  )
)
ensemble <- caretEnsemble(models)
summary(ensemble)

Loading required package: lattice
Loading required package: ggplot2
Loading required package: foreach
Loading required package: iterators
Loading required package: parallel

Attaching package: ‘caretEnsemble’

The following object is masked from ‘package:ggplot2’:

    autoplot

       V1                V2                V3                V4         
 Min.   :0.00150   Min.   :0.00060   Min.   :0.00150   Min.   :0.00580  
 1st Qu.:0.01335   1st Qu.:0.01645   1st Qu.:0.01895   1st Qu.:0.02438  
 Median :0.02280   Median :0.03080   Median :0.03430   Median :0.04405  
 Mean   :0.02916   Mean   :0.03844   Mean   :0.04383   Mean   :0.05389  
 3rd Qu.:0.03555   3rd Qu.:0.04795   3rd Qu.:0.05795   3rd Qu.:0.06450  
 Max.   :0.13710   Max.   :0.23390   Max.   :0.30590   Max.   :0.42640  
       V5                V6                V7               V8         
 Min.   :0.00670   Min.   :0.01020   Min.   :0.0033   Min.   :0.00550  
 1st Qu.:0.03805   1st Qu.:0.06703   1st Qu.:0.0809   1st Qu.:0.08042  
 Median :0.06250   Median :0.09215   Median :0.1070   Median :0.11210  
 Mean   :0.07520   Mean   :0.10457   Mean   :0.1217   Mean   :0.13480  
 3rd Qu.:0.10028   3rd Qu.:0.13412   3rd Qu.:0.1540   3rd Qu.:0.16960  
 Max.   :0.40100   Max.   :0.38230   Max.   :0.3729   Max.   :0.45900  
       V9               V10              V11              V12        
 Min.   :0.00750   Min.   :0.0113   Min.   :0.0289   Min.   :0.0236  
 1st Qu.:0.09703   1st Qu.:0.1113   1st Qu.:0.1293   1st Qu.:0.1335  
 Median :0.15225   Median :0.1824   Median :0.2248   Median :0.2490  
 Mean   :0.17800   Mean   :0.2083   Mean   :0.2360   Mean   :0.2502  
 3rd Qu.:0.23342   3rd Qu.:0.2687   3rd Qu.:0.3016   3rd Qu.:0.3312  
 Max.   :0.68280   Max.   :0.7106   Max.   :0.7342   Max.   :0.7060  
      V13              V14              V15              V16        
 Min.   :0.0184   Min.   :0.0273   Min.   :0.0031   Min.   :0.0162  
 1st Qu.:0.1661   1st Qu.:0.1752   1st Qu.:0.1646   1st Qu.:0.1963  
 Median :0.2640   Median :0.2811   Median :0.2817   Median :0.3047  
 Mean   :0.2733   Mean   :0.2966   Mean   :0.3202   Mean   :0.3785  
 3rd Qu.:0.3513   3rd Qu.:0.3862   3rd Qu.:0.4529   3rd Qu.:0.5357  
 Max.   :0.7131   Max.   :0.9970   Max.   :1.0000   Max.   :0.9988  
      V17              V18              V19              V20        
 Min.   :0.0349   Min.   :0.0375   Min.   :0.0494   Min.   :0.0656  
 1st Qu.:0.2059   1st Qu.:0.2421   1st Qu.:0.2991   1st Qu.:0.3506  
 Median :0.3084   Median :0.3683   Median :0.4350   Median :0.5425  
 Mean   :0.4160   Mean   :0.4523   Mean   :0.5048   Mean   :0.5630  
 3rd Qu.:0.6594   3rd Qu.:0.6791   3rd Qu.:0.7314   3rd Qu.:0.8093  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
      V21              V22              V23              V24        
 Min.   :0.0512   Min.   :0.0219   Min.   :0.0563   Min.   :0.0239  
 1st Qu.:0.3997   1st Qu.:0.4069   1st Qu.:0.4502   1st Qu.:0.5407  
 Median :0.6177   Median :0.6649   Median :0.6997   Median :0.6985  
 Mean   :0.6091   Mean   :0.6243   Mean   :0.6470   Mean   :0.6727  
 3rd Qu.:0.8170   3rd Qu.:0.8320   3rd Qu.:0.8486   3rd Qu.:0.8722  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
      V25              V26              V27              V28        
 Min.   :0.0240   Min.   :0.0921   Min.   :0.0481   Min.   :0.0284  
 1st Qu.:0.5258   1st Qu.:0.5442   1st Qu.:0.5319   1st Qu.:0.5348  
 Median :0.7211   Median :0.7545   Median :0.7456   Median :0.7319  
 Mean   :0.6754   Mean   :0.6999   Mean   :0.7022   Mean   :0.6940  
 3rd Qu.:0.8737   3rd Qu.:0.8938   3rd Qu.:0.9171   3rd Qu.:0.9003  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
      V29              V30              V31              V32        
 Min.   :0.0144   Min.   :0.0613   Min.   :0.0482   Min.   :0.0404  
 1st Qu.:0.4637   1st Qu.:0.4114   1st Qu.:0.3456   1st Qu.:0.2814  
 Median :0.6808   Median :0.6071   Median :0.4904   Median :0.4296  
 Mean   :0.6421   Mean   :0.5809   Mean   :0.5045   Mean   :0.4390  
 3rd Qu.:0.8521   3rd Qu.:0.7352   3rd Qu.:0.6420   3rd Qu.:0.5803  
 Max.   :1.0000   Max.   :1.0000   Max.   :0.9657   Max.   :0.9306  
      V33              V34              V35              V36        
 Min.   :0.0477   Min.   :0.0212   Min.   :0.0223   Min.   :0.0080  
 1st Qu.:0.2579   1st Qu.:0.2176   1st Qu.:0.1794   1st Qu.:0.1543  
 Median :0.3912   Median :0.3510   Median :0.3127   Median :0.3211  
 Mean   :0.4172   Mean   :0.4032   Mean   :0.3926   Mean   :0.3848  
 3rd Qu.:0.5561   3rd Qu.:0.5961   3rd Qu.:0.5934   3rd Qu.:0.5565  
 Max.   :1.0000   Max.   :0.9647   Max.   :1.0000   Max.   :1.0000  
      V37              V38              V39              V40        
 Min.   :0.0351   Min.   :0.0383   Min.   :0.0371   Min.   :0.0117  
 1st Qu.:0.1601   1st Qu.:0.1743   1st Qu.:0.1740   1st Qu.:0.1865  
 Median :0.3063   Median :0.3127   Median :0.2835   Median :0.2781  
 Mean   :0.3638   Mean   :0.3397   Mean   :0.3258   Mean   :0.3112  
 3rd Qu.:0.5189   3rd Qu.:0.4405   3rd Qu.:0.4349   3rd Qu.:0.4244  
 Max.   :0.9497   Max.   :1.0000   Max.   :0.9857   Max.   :0.9297  
      V41              V42              V43              V44        
 Min.   :0.0360   Min.   :0.0056   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.1631   1st Qu.:0.1589   1st Qu.:0.1552   1st Qu.:0.1269  
 Median :0.2595   Median :0.2451   Median :0.2225   Median :0.1777  
 Mean   :0.2893   Mean   :0.2783   Mean   :0.2465   Mean   :0.2141  
 3rd Qu.:0.3875   3rd Qu.:0.3842   3rd Qu.:0.3245   3rd Qu.:0.2717  
 Max.   :0.8995   Max.   :0.8246   Max.   :0.7733   Max.   :0.7762  
      V45               V46               V47               V48         
 Min.   :0.00000   Min.   :0.00000   Min.   :0.00000   Min.   :0.00000  
 1st Qu.:0.09448   1st Qu.:0.06855   1st Qu.:0.06425   1st Qu.:0.04512  
 Median :0.14800   Median :0.12135   Median :0.10165   Median :0.07810  
 Mean   :0.19723   Mean   :0.16063   Mean   :0.12245   Mean   :0.09142  
 3rd Qu.:0.23155   3rd Qu.:0.20037   3rd Qu.:0.15443   3rd Qu.:0.12010  
 Max.   :0.70340   Max.   :0.72920   Max.   :0.55220   Max.   :0.33390  
      V49               V50               V51                V52          
 Min.   :0.00000   Min.   :0.00000   Min.   :0.000000   Min.   :0.000800  
 1st Qu.:0.02635   1st Qu.:0.01155   1st Qu.:0.008425   1st Qu.:0.007275  
 Median :0.04470   Median :0.01790   Median :0.013900   Median :0.011400  
 Mean   :0.05193   Mean   :0.02042   Mean   :0.016069   Mean   :0.013420  
 3rd Qu.:0.06853   3rd Qu.:0.02527   3rd Qu.:0.020825   3rd Qu.:0.016725  
 Max.   :0.19810   Max.   :0.08250   Max.   :0.100400   Max.   :0.070900  
      V53                V54                V55               V56          
 Min.   :0.000500   Min.   :0.001000   Min.   :0.00060   Min.   :0.000400  
 1st Qu.:0.005075   1st Qu.:0.005375   1st Qu.:0.00415   1st Qu.:0.004400  
 Median :0.009550   Median :0.009300   Median :0.00750   Median :0.006850  
 Mean   :0.010709   Mean   :0.010941   Mean   :0.00929   Mean   :0.008222  
 3rd Qu.:0.014900   3rd Qu.:0.014500   3rd Qu.:0.01210   3rd Qu.:0.010575  
 Max.   :0.039000   Max.   :0.035200   Max.   :0.04470   Max.   :0.039400  
      V57               V58                V59                V60          
 Min.   :0.00030   Min.   :0.000300   Min.   :0.000100   Min.   :0.000600  
 1st Qu.:0.00370   1st Qu.:0.003600   1st Qu.:0.003675   1st Qu.:0.003100  
 Median :0.00595   Median :0.005800   Median :0.006400   Median :0.005300  
 Mean   :0.00782   Mean   :0.007949   Mean   :0.007941   Mean   :0.006507  
 3rd Qu.:0.01043   3rd Qu.:0.010350   3rd Qu.:0.010325   3rd Qu.:0.008525  
 Max.   :0.03550   Max.   :0.044000   Max.   :0.036400   Max.   :0.043900  
 Class  
 M:111  
 R: 97

Warning message:
“glm.fit: algorithm did not converge”Warning message:
“glm.fit: fitted probabilities numerically 0 or 1 occurred”

Call:
summary.resamples(object = results)

Models: SVM, CART, kNN, glm, lda 
Number of resamples: 30 

Accuracy 
          Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
SVM  0.7142857 0.8023810 0.8571429 0.8506638 0.9035714 0.9523810    0
CART 0.5500000 0.6666667 0.7142857 0.7157576 0.7619048 0.9047619    0
kNN  0.6500000 0.8196429 0.9000000 0.8699495 0.9090909 1.0000000    0
glm  0.5238095 0.6666667 0.7000000 0.7070635 0.7619048 0.9047619    0
lda  0.5714286 0.6666667 0.7500000 0.7444372 0.8095238 0.9523810    0

Kappa 
           Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
SVM  0.41121495 0.5934994 0.7096774 0.6950280 0.8049995 0.9049774    0
CART 0.04255319 0.3241273 0.4246455 0.4221056 0.5183179 0.8108108    0
kNN  0.30000000 0.6355114 0.7958971 0.7372650 0.8166667 1.0000000    0
glm  0.04545455 0.3273841 0.3999400 0.4113976 0.5234729 0.8090909    0
lda  0.13698630 0.3287671 0.5129665 0.4866521 0.6173061 0.9049774    0

Warning message in trControlCheck(x = trControl, y = target):
“x$savePredictions == TRUE is depreciated. Setting to 'final' instead.”Warning message in trControlCheck(x = trControl, y = target):
“indexes not defined in trControl.  Attempting to set them ourselves, so each model in the ensemble will have the same resampling indexes.”Warning message:
“glm.fit: algorithm did not converge”Warning message:
“glm.fit: fitted probabilities numerically 0 or 1 occurred”

The following models were ensembled: svmRadial, rpart, knn, glm, lda 
They were weighted: 
4.0191 -5.7612 0.085 -1.4433 -0.6825 0.2702
The resulting Accuracy is: 0.8778
The fit for each individual model on the Accuracy is: 
    method  Accuracy AccuracySD
 svmRadial 0.8669336 0.06281815
     rpart 0.7125397 0.09536742
       knn 0.8729004 0.06495796
       glm 0.7123521 0.11792499
       lda 0.7353752 0.09269090

	V1	V2	V3	V4	V5	V6	V7	V8	V9	V10	⋯	V51	V52	V53	V54	V55	V56	V57	V58	V59	V60
V1	1.00000000	0.735895604	0.57153661	0.49143751	0.3447966545	0.23892107	0.260814529	0.35552318	0.353419921	0.318275772	⋯	0.2544496830	0.355298662	0.3117294686	0.32229896	0.312067442	0.22064249	0.31372502	0.368131995	0.357116489	0.347077554
V2	0.73589560	1.000000000	0.77991587	0.60668448	0.4196689664	0.33232920	0.279040345	0.33461516	0.316733233	0.270781717	⋯	0.3205383646	0.434547562	0.3460764258	0.38395991	0.380164516	0.26226316	0.28034105	0.353041818	0.352199776	0.358761201
V3	0.57153661	0.779915872	1.00000000	0.78178597	0.5461413777	0.34627494	0.190434227	0.23788409	0.252691067	0.219637372	⋯	0.2381103505	0.394075754	0.3329137037	0.36718590	0.289730569	0.28766110	0.38081870	0.334108454	0.425047017	0.373948254
V4	0.49143751	0.606684483	0.78178597	1.00000000	0.7269434669	0.35280540	0.246440252	0.24674201	0.247077711	0.237768599	⋯	0.1746757917	0.374650635	0.3647717582	0.33421088	0.284954988	0.28093758	0.34025409	0.344864663	0.420265745	0.400626132
V5	0.34479665	0.419668966	0.54614138	0.72694347	1.0000000000	0.59705274	0.335421814	0.20400559	0.177905776	0.183218648	⋯	0.1159361127	0.266617167	0.3149851131	0.20530650	0.196472149	0.19932264	0.21939544	0.238792772	0.290981629	0.253709871
V6	0.23892107	0.332329200	0.34627494	0.35280540	0.5970527386	1.00000000	0.702889254	0.47168336	0.327578386	0.288621164	⋯	0.1717670563	0.252287930	0.1624036973	0.16407338	0.133464316	0.16675809	0.16133321	0.203985594	0.220573014	0.178157645
V7	0.26081453	0.279040345	0.19043423	0.24644025	0.3354218138	0.70288925	1.000000000	0.67577391	0.470579816	0.425447589	⋯	0.1841522309	0.144050509	0.0464028902	0.16307350	0.195540766	0.17414317	0.18632403	0.242645518	0.183578101	0.222492825
V8	0.35552318	0.334615160	0.23788409	0.24674201	0.2040055949	0.47168336	0.675773905	1.00000000	0.778576885	0.652524801	⋯	0.2606918260	0.219037753	0.1024471525	0.23400829	0.239551179	0.27681852	0.26721176	0.287603028	0.194400112	0.146216011
V9	0.35341992	0.316733233	0.25269107	0.24707771	0.1779057756	0.32757839	0.470579816	0.77857689	1.000000000	0.877130726	⋯	0.1748728686	0.207995601	0.1053521942	0.20261501	0.179341841	0.23276385	0.19396344	0.231744665	0.097292793	0.095243111
V10	0.31827577	0.270781717	0.21963737	0.23776860	0.1832186481	0.28862116	0.425447589	0.65252480	0.877130726	1.000000000	⋯	0.1670961541	0.165536968	0.0975435898	0.14672537	0.175254268	0.15188887	0.14032657	0.212276583	0.058273306	0.097358118
V11	0.34405764	0.297064686	0.27461039	0.27188142	0.2316836674	0.33357015	0.396588198	0.58458333	0.728062543	0.853140191	⋯	0.1576151651	0.165748448	0.0848007045	0.14257177	0.228991200	0.12233172	0.10340512	0.193357860	0.067726119	0.089695289
V12	0.21086119	0.194102177	0.21480700	0.17538061	0.2116571016	0.34445130	0.274431820	0.32832892	0.363404422	0.485392006	⋯	0.1134177418	0.117698589	0.0422627087	0.07845663	0.164590062	0.11565820	0.03073237	0.065273243	0.044613744	0.071363676
V13	0.21072220	0.249595669	0.25876684	0.21575445	0.2990864387	0.41110666	0.365390857	0.32295071	0.316899047	0.405369994	⋯	0.2033473921	0.147479474	0.0585993174	0.16091632	0.272492318	0.18374288	0.05786973	0.171139576	0.151803914	0.061410521
V14	0.25627774	0.273170131	0.29172413	0.28670752	0.3590619268	0.39623344	0.409576141	0.38711385	0.329659423	0.345683719	⋯	0.1804642968	0.137442874	0.1331956381	0.21092465	0.326821083	0.25216613	0.19088648	0.258675241	0.209121827	0.120966309
V15	0.30487810	0.307599462	0.28566302	0.27852925	0.3180591864	0.36790784	0.411691671	0.39151445	0.299575195	0.294698944	⋯	0.1531616994	0.135270923	0.1034439236	0.21870310	0.261822280	0.21839483	0.20251122	0.225545159	0.193670535	0.171088686
V16	0.23907924	0.261844403	0.23701680	0.24824531	0.3287248282	0.35378282	0.363086022	0.32223717	0.241818874	0.242869475	⋯	0.0998923335	0.104039035	0.0963247673	0.20692218	0.240967690	0.21547817	0.19173571	0.198019275	0.182336895	0.158438349
V17	0.13784532	0.152169829	0.20109316	0.22320254	0.3264772001	0.29318975	0.250023865	0.14091227	0.100145858	0.121264326	⋯	0.0090361467	0.020312871	0.0356350738	0.12913823	0.168460108	0.12896832	0.14570835	0.148562980	0.121800111	0.093991989
V18	0.04181749	0.042870375	0.12058709	0.19499189	0.2992659908	0.23577840	0.208056627	0.06133332	0.027379524	0.063745438	⋯	-0.1046557328	-0.057235815	-0.0066270165	0.07234421	0.093766845	0.08081248	0.05693014	0.096021680	0.028445569	0.046616986
V19	0.05522719	0.040910750	0.09930269	0.18940451	0.3405427387	0.22630485	0.215494622	0.06182527	0.067237280	0.099632336	⋯	-0.0509877706	0.011449859	0.0513672005	0.12015274	0.099081852	0.12133071	0.04520378	0.138364901	0.023019468	0.007467933
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V37	0.11956546	0.169185954	0.10752983	0.06348570	-0.0646169136	-0.06479768	-0.001375728	0.11073852	0.111768868	0.085071886	⋯	-0.0282905172	0.002078041	0.0797988842	0.13042749	0.086914414	0.11654872	0.18078889	0.110760434	0.163161660	0.166263051
V38	0.20987338	0.217493567	0.13027599	0.08988690	-0.0086204624	-0.04874532	0.065900108	0.18660873	0.223982643	0.175717327	⋯	0.0942053770	0.134015075	0.1711038222	0.20693068	0.235457137	0.21758740	0.15632038	0.169710465	0.206000945	0.233287980
V39	0.20837105	0.186828029	0.11049866	0.08934585	0.0634082531	0.03059882	0.080941702	0.20614548	0.211897320	0.233832857	⋯	0.1240380780	0.108563890	0.1675993997	0.20011580	0.294578157	0.22313310	0.14313081	0.218912490	0.231149772	0.222610988
V40	0.09999307	0.098349865	0.07413698	0.04514050	0.0616156266	0.08111878	0.112673483	0.18441111	0.122734860	0.177357346	⋯	0.0666730272	0.042677450	0.1283098942	0.12138111	0.157434907	0.15070020	0.10560298	0.143717671	0.189058257	0.202033603
V41	0.12731315	0.188226222	0.18904675	0.14524144	0.0988318238	0.07579689	0.041070798	0.09751670	0.019589175	-0.002522934	⋯	0.2774710588	0.255774004	0.2540642017	0.18157896	0.177850711	0.22066960	0.19353186	0.196281933	0.304520537	0.281889287
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V43	0.20605736	0.186368171	0.11392033	0.05062897	0.0637057610	0.03438018	-0.025727075	0.11472051	0.052409087	0.076137748	⋯	0.3971902594	0.302861357	0.2532032712	0.15533870	0.097670527	0.12357400	0.10412032	0.210814096	0.199333537	0.161415854
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V45	0.27996783	0.285715977	0.18073379	0.08782352	0.0892019954	0.08546800	0.110813334	0.24017633	0.320573040	0.287459073	⋯	0.4169733623	0.350208464	0.1812921421	0.16287941	0.242756595	0.17074981	0.14428119	0.167336863	0.178401730	0.157181367
V46	0.31935417	0.304246991	0.17364947	0.08001232	0.0819636737	0.02952413	0.076537392	0.16909883	0.195446821	0.138446740	⋯	0.5053040085	0.429308856	0.2369707642	0.18796426	0.269119020	0.17818183	0.16212509	0.237890366	0.205290771	0.180690938
V47	0.23034309	0.255797259	0.17952794	0.04610851	0.0414192669	0.01664050	0.098924921	0.10974413	0.084190934	0.090661567	⋯	0.5705747748	0.398599815	0.2069700885	0.15992002	0.194223424	0.14604206	0.15781492	0.240470822	0.209045200	0.139726958
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V49	0.24756021	0.313995237	0.22307411	0.13329406	0.0881278448	0.08072878	0.194719797	0.27142187	0.222135267	0.264885244	⋯	0.5260948048	0.319286248	0.1508706679	0.19582594	0.230032724	0.15518623	0.17309819	0.328238383	0.209151854	0.088640372
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V55	0.31206744	0.380164516	0.28973057	0.28495499	0.1964721487	0.13346432	0.195540766	0.23955118	0.179341841	0.175254268	⋯	0.2789351170	0.337580658	0.3156555863	0.45505891	1.000000000	0.42994818	0.38720438	0.503464861	0.453658123	0.264399201
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V57	0.31372502	0.280341046	0.38081870	0.34025409	0.2193954389	0.16133321	0.186324030	0.26721176	0.193963443	0.140326569	⋯	0.1914070616	0.191264022	0.3081969253	0.36144280	0.387204379	0.51515432	1.00000000	0.509804942	0.431295271	0.287218633
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V60	0.34707755	0.358761201	0.37394825	0.40062613	0.2537098705	0.17815765	0.222492825	0.14621601	0.095243111	0.097358118	⋯	0.2467644850	0.195378585	0.2807802354	0.28347080	0.264399201	0.34944936	0.28721863	0.329826737	0.642872023	1.000000000

	freq	percentage
M	111	53.36538
R	97	46.63462