| Title: | 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. |
| Authors: | Charles Bouveyron & Stephane Girard |
| Maintainer: | Charles Bouveyron <[email protected]> |
| License: | GPL-2 |
| Version: | 1.2 |
| Built: | 2024-11-23 06:28:50 UTC |
| Source: | CRAN |
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.
| Package: | robustDA |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2014-09-26 |
| License: | GPL-2 |
Charles Bouveyron & Stéphane Girard Maintainer: Charles Bouveyron <[email protected]>
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.
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$cls == Y.cls) / length(Y.cls),"\n")set.seed(12345) ## Simulated data N = 600 n = N/4 S1 = S2 = S3 = S4 = 2*diag(2) m1 = 1.5*c(-4,0) m4 = 1.5*c(0,-4) m3 = 1.5*c(0,4) m2 = 1.5*c(4,0) Z.data = rbind(mvrnorm(n,m1,S1),mvrnorm(n,m2,S2), mvrnorm(n,m3,S3),mvrnorm(n,m4,S4)) Z.cls = c(rep(1,n),rep(1,n),rep(2,n),rep(2,n)) # Split in training and test sets ind = sample(1:N,N) X.data = Z.data[ind[1:(3*N/4)],] X.cls = Z.cls[ind[1:(3*N/4)]] Y.data = Z.data[ind[(3*N/4+1):N],] Y.cls = Z.cls[ind[(3*N/4+1):N]] ## Adding noise label cls = X.cls nois = rbinom(length(cls),1,0.3) lbl = cls lbl[cls==1 & nois] = 2 lbl[cls==2 & nois] = 1 # Plot par(mfrow=c(2,2)) plot(X.data,col=X.cls,pch=(18:19)[X.cls], main='Learning set with actual labels',xlab='',ylab='') plot(X.data,col=lbl,pch=(18:19)[lbl], main='Learning set with noisy labels',xlab='',ylab='') ## Classification with LDA c.lda = lda(X.data,lbl) res.lda <- predict(c.lda,Y.data)$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")
The prediction method for 'rmda' class objects which allows to predict the labels for test observations.
## S3 method for class 'rmda' predict(object, X, ...)## S3 method for class 'rmda' predict(object, X, ...)
object |
a supervised classifier genarated by the rmda function (a 'rmda' object). |
X |
the test data. |
... |
additional options for internal functions. |
A list with:
- cls: the predicted class labels,
- P: the posterior probabilities that observations belong to the classes.
Charles Bouveyron & Stéphane Girard
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.
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$cls == Y.cls) / length(Y.cls),"\n")set.seed(12345) ## Simulated data N = 600 n = N/4 S1 = S2 = S3 = S4 = 2*diag(2) m1 = 1.5*c(-4,0) m4 = 1.5*c(0,-4) m3 = 1.5*c(0,4) m2 = 1.5*c(4,0) Z.data = rbind(mvrnorm(n,m1,S1),mvrnorm(n,m2,S2), mvrnorm(n,m3,S3),mvrnorm(n,m4,S4)) Z.cls = c(rep(1,n),rep(1,n),rep(2,n),rep(2,n)) # Split in training and test sets ind = sample(1:N,N) X.data = Z.data[ind[1:(3*N/4)],] X.cls = Z.cls[ind[1:(3*N/4)]] Y.data = Z.data[ind[(3*N/4+1):N],] Y.cls = Z.cls[ind[(3*N/4+1):N]] ## Adding noise label cls = X.cls nois = rbinom(length(cls),1,0.3) lbl = cls lbl[cls==1 & nois] = 2 lbl[cls==2 & nois] = 1 # Plot par(mfrow=c(2,2)) plot(X.data,col=X.cls,pch=(18:19)[X.cls], main='Learning set with actual labels',xlab='',ylab='') plot(X.data,col=lbl,pch=(18:19)[lbl], main='Learning set with noisy labels',xlab='',ylab='') ## Classification with LDA c.lda = lda(X.data,lbl) res.lda <- predict(c.lda,Y.data)$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")
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.
rmda(X, cls, K = 4, model = "VEV")rmda(X, cls, K = 4, model = "VEV")
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). |
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.
Charles Bouveyron & Stéphane Girard
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.
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$cls == Y.cls) / length(Y.cls),"\n")set.seed(12345) ## Simulated data N = 600 n = N/4 S1 = S2 = S3 = S4 = 2*diag(2) m1 = 1.5*c(-4,0) m4 = 1.5*c(0,-4) m3 = 1.5*c(0,4) m2 = 1.5*c(4,0) Z.data = rbind(mvrnorm(n,m1,S1),mvrnorm(n,m2,S2), mvrnorm(n,m3,S3),mvrnorm(n,m4,S4)) Z.cls = c(rep(1,n),rep(1,n),rep(2,n),rep(2,n)) # Split in training and test sets ind = sample(1:N,N) X.data = Z.data[ind[1:(3*N/4)],] X.cls = Z.cls[ind[1:(3*N/4)]] Y.data = Z.data[ind[(3*N/4+1):N],] Y.cls = Z.cls[ind[(3*N/4+1):N]] ## Adding noise label cls = X.cls nois = rbinom(length(cls),1,0.3) lbl = cls lbl[cls==1 & nois] = 2 lbl[cls==2 & nois] = 1 # Plot par(mfrow=c(2,2)) plot(X.data,col=X.cls,pch=(18:19)[X.cls], main='Learning set with actual labels',xlab='',ylab='') plot(X.data,col=lbl,pch=(18:19)[lbl], main='Learning set with noisy labels',xlab='',ylab='') ## Classification with LDA c.lda = lda(X.data,lbl) res.lda <- predict(c.lda,Y.data)$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")