adaptDA (version 1.0)

amdat: Adaptive Mixture Discriminant Analysis (transductive approach)

Description

The adaptive mixture discriminant analysis (AMDA) allows to adapt a model-based classifier to the situation a class represented in the test set may have not been encountered earlier in the learning phase.

Usage

amdat(X, cls, Y, K, model = "qda", maxit = 25, eps = 1e-04, ...)

Arguments

X

the learning data

cls

the known labels for the learning data

Y

the test data.

K

the number of expected classes in the test set.

model

the model to be used among "qda" or "lda". The default model is "qda".

maxit

the maximum number of iterations for the EM algorithm.

eps

the threshold value for the likelihood differences to stop the EM algorithm.

...

additional parameters for internal functions.

Value

A list is returned with the following fields:

model

the used model

mean

the updated mixture means

prop

the updated mixture proportions

var

the updated mixture covariance matrices

cls

the predicted labels for the test data

P

the posterior probabilities

crit

the criterion values for AIC, BIC and ICL

References

C. Bouveyron, Adaptive mixture discriminant analysis for supervised learning with unobserved classes, Journal of Classification, vol. 31(1), pp. 49-84, 2014.

Examples

set.seed(12345)

## Data simulation
data(iris)
Z.data = iris[,-5]
Z.cls = as.numeric(iris[,5])
Z.cls[as.numeric(iris[,5]==2)] = 3
Z.cls[as.numeric(iris[,5]==3)] = 2
N = 150

## Sampling
ind = sample(1:N,N)
X.data = Z.data[ind[1:(2*N/3)],]
X.cls = Z.cls[ind[1:(2*N/3)]]
X.data = X.data[X.cls!=3,]
X.cls = X.cls[X.cls!=3]
Y.data = Z.data[ind[(2*N/3+1):N],]
Y.cls = Z.cls[ind[(2*N/3+1):N]]

# Plotting the data
par(mfrow=c(2,3))#,cex.lab=0.75,cex.axis=0.75,cex.main=0.75,cex.sub=0.75)
pc = princomp(Z.data)
x = predict(pc,X.data)
y = predict(pc,Y.data)
plot(y,type='n',main='Learning data')
points(x[,1:2],col=X.cls+1,pch=19,main='Learning data')
y = predict(pc,Y.data)
plot(y[,1:2],col=1,pch=19,main='Test data')
plot(y[,1:2],col=Y.cls+1,pch=19,main='True labels of test data')

## Usual classification with QDA
c1 = qda(X.data,X.cls)
res1 = predict(c1,Y.data)
plot(y[,1:2],col=as.numeric(res1$class)+1,pch=19,main='QDA results')

## Classification with AMDAt
B = rep(c(-Inf),7)
myPRMS <- vector(mode='list', length=7) # vector of lists!
for (i in 2:5){
 myPRMS[[i]] = amdat(X.data,X.cls,Y.data,K=i)
 B[i] = myPRMS[[i]]$crit$aic
}
plot(2:5,B[2:5],type='b',xlab='Nb of components',ylab='AIC value',main='AIC values for AMDAt')
res2 = myPRMS[[which.max(B)]]
plot(y[,1:2],col=res2$cls+1,pch=19,main='AMDAt results')

## Classification results
cat("* Correct classification rates :\n")
cat("\tQDA:\t",sum(res1$class == Y.cls) / length(Y.cls),"\n")
print(table(res1$class,Y.cls))
cat("\tAMDAt:\t",sum(res2$cls == Y.cls) / length(Y.cls),"\n")
print(table(res2$cls,Y.cls))