rmda {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.

Usage

rmda(X, cls, K = 4, model = "VEV")

Arguments

X

the data.

cls

the known labels.

K

the total number of groups which are assumed to exist within the known classes.

model

the model name (according to the Mclust nomenclature).

Value

An object of class "rmda" with: - K: the total number of groups, - prms: all model parameters as returned by Mclust, - R: the posterior probabilities that the fitted groups belong to the known classes.

Author(s)

Charles Bouveyron & Stéphane Girard

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")