robustDA-package {robustDA}

Robust Mixture Discriminant Analysis

Description

Robust mixture discriminant analysis (RMDA), proposed in Bouveyron & Girard, 2009 <doi:10.1016/j.patcog.2009.03.027>, allows to build a robust supervised classifier from learning data with label noise. The idea of the proposed method is to confront an unsupervised modeling of the data with the supervised information carried by the labels of the learning data in order to detect inconsistencies. The method is able afterward to build a robust classifier taking into account the detected inconsistencies into the labels.

Details

Package:	robustDA
Type:	Package
Version:	1.0
Date:	2014-09-26
License:	GPL-2

Author(s)

Charles Bouveyron & Stéphane Girard Maintainer: Charles Bouveyron <[e-mail]>

References

C. Bouveyron and S. Girard, Robust supervised classification with mixture models: Learning from data with uncertain labels, Pattern Recognition, vol. 42 (11), pp. 2649-2658, 2009.

Examples

set.seed(12345)

## Simulated data
N = 600
n = N/4
S1 = S2 = S3 = S4 = 2*diag(2)
m1 = 1.5*c(-4,0)
m4 = 1.5*c(0,-4)
m3 = 1.5*c(0,4)
m2 = 1.5*c(4,0)
Z.data = rbind(mvrnorm(n,m1,S1),mvrnorm(n,m2,S2),
  mvrnorm(n,m3,S3),mvrnorm(n,m4,S4))
Z.cls = c(rep(1,n),rep(1,n),rep(2,n),rep(2,n))

# Split in training and test sets
ind = sample(1:N,N)
X.data = Z.data[ind[1:(3*N/4)],]
X.cls = Z.cls[ind[1:(3*N/4)]]
Y.data = Z.data[ind[(3*N/4+1):N],]
Y.cls = Z.cls[ind[(3*N/4+1):N]]

## Adding noise label
cls = X.cls
nois = rbinom(length(cls),1,0.3)
lbl = cls
lbl[cls==1 & nois] = 2
lbl[cls==2 & nois] = 1

# Plot
par(mfrow=c(2,2))
plot(X.data,col=X.cls,pch=(18:19)[X.cls],
  main='Learning set with actual labels',xlab='',ylab='')
plot(X.data,col=lbl,pch=(18:19)[lbl],
  main='Learning set with noisy labels',xlab='',ylab='')


## Classification with LDA
c.lda = lda(X.data,lbl)
res.lda <- predict(c.lda,Y.data)$class

## Classification with MDA
c.mda = MclustDA(X.data,lbl,G=2)
res.mda = predict(c.mda,Y.data)$cl
plot(Y.data,col=res.mda,pch=(18:19)[res.mda],
     main='Classification of test set with MDA',xlab='',ylab='')

## Classification with RMDA
c.rmda <- rmda(X.data,lbl,K=4,model='VEV')
res.rmda <- predict(c.rmda,Y.data)
plot(Y.data,col=res.rmda$cls,pch=(18:19)[res.rmda$cls],
     main='Classification of test set with RMDA',xlab='',ylab='')

## Classification results
cat("* Correct classification rates on test data:\n")
cat("\tLDA:\t",sum(res.lda == Y.cls) / length(Y.cls),"\n")
cat("\tMDA:\t",sum(res.mda == Y.cls) / length(Y.cls),"\n")
cat("\tRMDA:\t",sum(res.rmda$cls == Y.cls) / length(Y.cls),"\n")