adaptDA (version 1.0)

amdai: Adaptive Mixture Discriminant Analysis (inductive 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

amdai(X, cls, model = "qda")

Arguments

X

the learning data

cls

the known labels for the learning data

model

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

Value

the function returns a QDA or LDA classifier to be used within the predict function.

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 AMDAi
c2 = amdai(X.data,X.cls,model='qda')
B = rep(c(-Inf),5)
myPRMS <- vector(mode='list', length=7) # vector of lists!
for (i in 2:5){
  myPRMS[[i]] = predict(c2,Y.data,K=i)
	B[i] = myPRMS[[i]]$crit$bic
}
plot(2:5,B[2:5],type='b',xlab='Nb of components',ylab='AIC value',main='AIC values for AMDA')
res2 = myPRMS[[which.max(B)]]
plot(y[,1:2],col=res2$cls+1,pch=19,main='AMDA 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("\tAMDAi:\t",sum(res2$cls == Y.cls) / length(Y.cls),"\n")
print(table(res2$cls,Y.cls))