Video 2

Classification


Before we start, please install the following packages:


2.1. Classification by logistic regression

We can use logistic regression for classification: try glm with family="binomial". Let’s test on predicting mouse sex by weight.

Mice = read.table("http://edu.sablab.net/data/txt/mice.txt",header=T,sep="\t",as.is=FALSE)
str(Mice)
## 'data.frame':    790 obs. of  14 variables:
##  $ ID                  : int  1 2 3 368 369 370 371 372 4 5 ...
##  $ Strain              : Factor w/ 40 levels "129S1/SvImJ",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Sex                 : Factor w/ 2 levels "f","m": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Starting.age        : int  66 66 66 72 72 72 72 72 66 66 ...
##  $ Ending.age          : int  116 116 108 114 115 116 119 122 109 112 ...
##  $ Starting.weight     : num  19.3 19.1 17.9 18.3 20.2 18.8 19.4 18.3 17.2 19.7 ...
##  $ Ending.weight       : num  20.5 20.8 19.8 21 21.9 22.1 21.3 20.1 18.9 21.3 ...
##  $ Weight.change       : num  1.06 1.09 1.11 1.15 1.08 ...
##  $ Bleeding.time       : int  64 78 90 65 55 NA 49 73 41 129 ...
##  $ Ionized.Ca.in.blood : num  1.2 1.15 1.16 1.26 1.23 1.21 1.24 1.17 1.25 1.14 ...
##  $ Blood.pH            : num  7.24 7.27 7.26 7.22 7.3 7.28 7.24 7.19 7.29 7.22 ...
##  $ Bone.mineral.density: num  0.0605 0.0553 0.0546 0.0599 0.0623 0.0626 0.0632 0.0592 0.0513 0.0501 ...
##  $ Lean.tissues.weight : num  14.5 13.9 13.8 15.4 15.6 16.4 16.6 16 14 16.3 ...
##  $ Fat.weight          : num  4.4 4.4 2.9 4.2 4.3 4.3 5.4 4.1 3.2 5.2 ...
## let's remove animals with NA values
ikeep = apply(is.na(Mice),1,sum) == 0

## all variables except strain
mod0 = glm(Sex ~ .-Strain, data = Mice[ikeep,], family = "binomial")
summary(mod0)
## 
## Call:
## glm(formula = Sex ~ . - Strain, family = "binomial", data = Mice[ikeep, 
##     ])
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -2.32688  -0.67541   0.05338   0.60108   2.92236  
## 
## Coefficients:
##                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           7.714e+01  1.246e+01   6.189 6.07e-10 ***
## ID                   -7.552e-04  3.939e-04  -1.917 0.055213 .  
## Starting.age          9.787e-03  2.302e-02   0.425 0.670684    
## Ending.age            1.320e-02  1.717e-02   0.769 0.441899    
## Starting.weight      -4.338e-01  2.170e-01  -1.999 0.045574 *  
## Ending.weight         6.482e-01  2.026e-01   3.199 0.001380 ** 
## Weight.change        -1.106e+01  4.379e+00  -2.525 0.011554 *  
## Bleeding.time        -5.441e-04  3.645e-03  -0.149 0.881344    
## Ionized.Ca.in.blood  -1.748e+00  1.707e+00  -1.024 0.305788    
## Blood.pH             -7.996e+00  1.588e+00  -5.035 4.79e-07 ***
## Bone.mineral.density -3.026e+02  2.624e+01 -11.531  < 2e-16 ***
## Lean.tissues.weight   1.935e-01  5.064e-02   3.820 0.000133 ***
## Fat.weight           -2.504e-02  4.502e-02  -0.556 0.578098    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1052.19  on 758  degrees of freedom
## Residual deviance:  639.57  on 746  degrees of freedom
## AIC: 665.57
## 
## Number of Fisher Scoring iterations: 5
## only significant
mod1 = glm(Sex ~ Blood.pH + Bone.mineral.density + Lean.tissues.weight + Ending.weight, 
           data = Mice[ikeep,], family = "binomial")
summary(mod1)
## 
## Call:
## glm(formula = Sex ~ Blood.pH + Bone.mineral.density + Lean.tissues.weight + 
##     Ending.weight, family = "binomial", data = Mice[ikeep, ])
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.1658  -0.6716   0.0702   0.6456   2.9113  
## 
## Coefficients:
##                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)            60.30264   10.49961   5.743 9.28e-09 ***
## Blood.pH               -7.49819    1.44791  -5.179 2.24e-07 ***
## Bone.mineral.density -277.92619   24.35660 -11.411  < 2e-16 ***
## Lean.tissues.weight     0.20197    0.04674   4.321 1.55e-05 ***
## Ending.weight           0.21222    0.03255   6.519 7.09e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1052.19  on 758  degrees of freedom
## Residual deviance:  664.25  on 754  degrees of freedom
## AIC: 674.25
## 
## Number of Fisher Scoring iterations: 5
##load some functions for ML:
source("http://r.modas.lu/LibML.r")
## [1] "----------------------------------------------------------------"
## [1] "libML: Machine learning library"
## [1] "Needed:"
## [1] "randomForest" "e1071"       
## [1] "Absent:"
## character(0)
##predict values (this is not informative! We work on training set!)
x = predict(mod1, Mice[ikeep,],  type="response")
x = factor(levels(Mice$Sex)[1+as.integer(x >0.5)],levels = levels(Mice$Sex))
CM = getConfusionMatrix(Mice$Sex[ikeep],x)
print(CM)
##          f   m
## pred.f 300  82
## pred.m  78 299
cat("Accuracy =",1 - getMCError(CM),"\n")
## Accuracy = 0.7891963

To test classification one should use independent training and test sets. One method - n-fold crossvalidation. We will use warp-up from LibML.r

Y = Mice[ikeep,"Sex"]
X = Mice[ikeep,c("Blood.pH","Bone.mineral.density", "Lean.tissues.weight", "Ending.weight")]

res = runCrossValidation(X,Y,method = "glm")
str(res)
## List of 14
##  $ method        : chr "glm"
##  $ nfold         : num 5
##  $ ntry          : num 10
##  $ error         : num 0.218
##  $ accuracy      : num 0.782
##  $ b_error       : num 0.218
##  $ b_accuracy    : num 0.782
##  $ specificity   : num 0.782
##  $ sensitivity   : num 0.782
##  $ CM            : num [1:2, 1:2] 297.5 80.5 84.6 296.4
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:2] "pred.f" "pred.m"
##   .. ..$ : chr [1:2] "f" "m"
##  $ sd.error      : num 0.00405
##  $ sd.accuracy   : num 0.00405
##  $ sd.specificity: num 0.00404
##  $ sd.sensitivity: num 0.00404
res$CM
##            f     m
## pred.f 297.5  84.6
## pred.m  80.5 296.4
res$accuracy
## [1] 0.7824769

2.2. Feature selections: ROC curve and AUC

Let’s consider iris dataset

library(caTools)
plot(iris[,-5],col = iris[,5],pch=19)

par(mfcol=c(2,2))
for (ipred in 1:4){
  plot(density(iris[as.integer(iris[,5])==1,ipred]),
       xlim=c(min(iris[,ipred]),max(iris[,ipred])),
       col=1,lwd=2,main=names(iris)[ipred])
  lines(density(iris[as.integer(iris[,5])==2,ipred]),col=2,lwd=2)
  lines(density(iris[as.integer(iris[,5])==3,ipred]),col=3,lwd=2)
}

par(mfcol=c(2,2))
colAUC(iris[,"Sepal.Length"],iris[,"Species"],plotROC=T)
##                            [,1]
## setosa vs. versicolor    0.9326
## setosa vs. virginica     0.9846
## versicolor vs. virginica 0.7896
colAUC(iris[,"Sepal.Width"],iris[,"Species"],plotROC=T)
##                            [,1]
## setosa vs. versicolor    0.9248
## setosa vs. virginica     0.8344
## versicolor vs. virginica 0.6636
colAUC(iris[,"Petal.Length"],iris[,"Species"],plotROC=T)
##                            [,1]
## setosa vs. versicolor    1.0000
## setosa vs. virginica     1.0000
## versicolor vs. virginica 0.9822
colAUC(iris[,"Petal.Width"],iris[,"Species"],plotROC=T)

##                            [,1]
## setosa vs. versicolor    1.0000
## setosa vs. virginica     1.0000
## versicolor vs. virginica 0.9804

Another example: lung squamous cell carcinoma SCC. Here we should find the gene with the top predictive potential. Let’s use AUC.

source("http://r.modas.lu/readAMD.r")  
SCC = readAMD("http://edu.modas.lu/data/txt/scc_data.txt",
              stringsAsFactors=TRUE,
              index.column=1,
              sum.func="mean")
## [1] "Repeated feature IDs => data are summarized (mean) by row"
## [1] "Performing summarization: 17641 rows -> 17318 rows by <mean>"
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  |======================================================================| 100%[1] "done in"
## Time difference of 0.4047918 secs
str(SCC)
## List of 5
##  $ ncol: int 36
##  $ nrow: int 17318
##  $ anno:'data.frame':    17318 obs. of  2 variables:
##   ..$ ID  : chr [1:17318] "A1BG" "A1CF" "A2BP1" "A2LD1" ...
##   ..$ Name: chr [1:17318] "NM_130786 // A1BG // alpha-1-B glycoprotein // 19q13.4 // 1 /// ENST00000263100 " "NM_138933 // A1CF // APOBEC1 complementation factor // 10q11.23 // 29974 /// NM_" "NM_018723 // A2BP1 // ataxin 2-binding protein 1 // 16p13.3 // 54715 /// NM_1458,ENST00000432184 // A2BP1 // at"| __truncated__ "NM_033110 // A2LD1 // AIG2-like domain 1 // 13q32.3 // 87769 /// ENST00000376250" ...
##  $ meta:'data.frame':    36 obs. of  1 variable:
##   ..$ State: Factor w/ 2 levels "cancer","normal": 1 1 1 1 1 1 1 1 1 1 ...
##  $ X   : num [1:17318, 1:36] 5.28 3.95 3.82 5.56 10.33 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:17318] "A1BG" "A1CF" "A2BP1" "A2LD1" ...
##   .. ..$ : chr [1:36] "Cancer.1" "Cancer.2" "Cancer.3" "Cancer.4" ...
## colAUC gives a matrix
AUC = colAUC(t(SCC$X),SCC$meta$State,plotROC=FALSE)

## to vector
AUC = AUC[1,]

par(mfcol=c(1,2))
## plot AUC density
plot(density(AUC),main="AUC for all genes")
## how many ideal genes
sum(AUC==1)
## [1] 973
## let's find gene with AUC=1 and maximal logFC
logFC = apply(SCC$X[,SCC$meta$State=="cancer"],1,mean) - apply(SCC$X[,SCC$meta$State=="normal"],1,mean)
logFC[AUC<1]=0
i = which.max(abs(logFC) * AUC)
barplot(SCC$X[i,],col=c(cancer="#FF8888",normal="#8888FF")[SCC$meta$State], pch=19,main=SCC$anno[i,1],las=2,cex.names=0.5)


2.3. Support Vector Machine (SVM) and Random Forest (RF)

Let us build and validate classifier.

  1. We need to divide dataset into training and test subsets. For example trainging set - 70% of flowers and test set - 30%.
  2. Train SVM on training data
  3. Make predictions for test data and calculate misclassification error

Use svm() for SVM and randomForest for RF.

#install.packages("e1071")
library(e1071)
## 
## Attaching package: 'e1071'
## The following objects are masked from 'package:PerformanceAnalytics':
## 
##     kurtosis, skewness
library(randomForest)
## randomForest 4.6-14
## Type rfNews() to see new features/changes/bug fixes.
itrain = sample(1:nrow(iris), 0.7 * nrow(iris) )
itest = (1:nrow(iris))[-itrain]

## SVM classifier
model1 = svm(Species ~ ., data = iris[itrain,])
## RF classifier
model2 = randomForest(Species ~ ., data = iris[itrain,])

## error on training set - should be small
pred.train = as.character(predict(model1,iris[itrain,-5]))
CM.train = getConfusionMatrix(iris[itrain,5], pred.train)
print(CM.train)
##                 setosa versicolor virginica
## pred.setosa         39          0         0
## pred.versicolor      0         38         3
## pred.virginica       0          0        25
getAccuracy(CM.train)
## [1] 0.9714286
## error on test set - much more important: SVM
pred.test = as.character(predict(model1,iris[itest,-5]))
CM.test = getConfusionMatrix(iris[itest,5], pred.test)
print(CM.test)
##                 setosa versicolor virginica
## pred.setosa         11          0         0
## pred.versicolor      0         12         3
## pred.virginica       0          0        19
getAccuracy(CM.test)
## [1] 0.9333333
## error on test set - much more important: RF
pred.test = as.character(predict(model2,iris[itest,-5]))
CM.test = getConfusionMatrix(iris[itest,5], pred.test)
print(CM.test)
##                 setosa versicolor virginica
## pred.setosa         11          0         0
## pred.versicolor      0         11         1
## pred.virginica       0          1        21
getAccuracy(CM.test)
## [1] 0.9555556

Or alternatively use a warp-up to to crossvalidation:

source("http://r.modas.lu/LibML.r")
## [1] "----------------------------------------------------------------"
## [1] "libML: Machine learning library"
## [1] "Needed:"
## [1] "randomForest" "e1071"       
## [1] "Absent:"
## character(0)
## iris example
res = runCrossValidation(iris[,-5],iris[,5],method = "svm")
res$accuracy
## [1] 0.96
## repeat: mice sex by logistic
res1 = runCrossValidation(X,Y,method = "glm")
res1$accuracy
## [1] 0.7844532
## repeat: mice sex by support vector machines
res2 = runCrossValidation(X,Y,method = "svm")
res2$accuracy
## [1] 0.7926219
## repeat: mice sex by random forest
res3 = runCrossValidation(X,Y,method = "rf")
res3$accuracy
## [1] 0.8118577

Let’s try to predict cell types for single cell data. This cannot be solved by logistic regression (not linearly-dividable).

Panc = read.table("http://edu.modas.lu/data/txt/tsne_normpancreas.txt",sep="\t",header=TRUE,row.names=1,as.is=FALSE)
str(Panc)
## 'data.frame':    2544 obs. of  7 variables:
##  $ individual        : Factor w/ 8 levels "DID_scRSq01",..: 4 4 4 4 4 4 4 4 4 4 ...
##  $ sex               : Factor w/ 2 levels "female","male": 2 2 2 2 2 2 2 2 2 2 ...
##  $ age               : int  21 21 21 21 21 21 21 21 21 21 ...
##  $ nreads            : int  447263 412082 167913 274448 323913 419043 600361 302079 262397 227087 ...
##  $ inferred.cell.type: Factor w/ 7 levels "acinar cell",..: 4 4 1 4 4 4 3 3 1 1 ...
##  $ tsne1             : num  33.2 32.6 20 31.8 31 ...
##  $ tsne2             : num  14 15.2 -51.6 14 16.4 ...
## color - inferred cell type
col = as.integer(Panc$inferred.cell.type)+1
## shape - individual
pch=13+as.integer(Panc$individual)
## plot & legend
plot(Panc$tsne1,Panc$tsne2,pch=pch,col=col,main="tSNE with Inferred Cell Type",xlim=c(-45,50))
legend("bottomright",levels(Panc$inferred.cell.type),pch=15,col=1+(1:nlevels(Panc$inferred.cell.type)))
legend("bottomleft","shape - patient")

Run this yourself:

## repeat: mice sex by support vector machines
resSVM = runCrossValidation(Panc[,c("tsne1","tsne2")],Panc$inferred.cell.type,method = "svm",echo=TRUE)
resSVM$accuracy

## repeat: mice sex by random forest
resRF = runCrossValidation(Panc[,c("tsne1","tsne2")],Panc$inferred.cell.type,method = "rf",echo=TRUE)
resRF$accuracy

resRF$CM

Exercise 2

  1. Please consider breast cancer dataset of Wisconsin University breastcancer. Please note, that the data are givein in CSV format (comma-separated values). Try building glm model to discriminate benign tumours (class=0) from malignant (class=1). Play with optimal numer of predictors. Exclude rows with NA values

glm, getMCError, predict, getConfusionMatrix, getAccuracy

  1. For task a - train now a classifier and report correctly calculated error. Try glm, svm, rf

runCrossValidation or sample, glm, svm, rf, predict, getConfusionMatrix, getMCError


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By Petr Nazarov