Nothing
#' @include LinearDiscriminantClassifier.R
setClass("EMLinearDiscriminantClassifier",
representation(responsibilities="matrix"),
prototype(name="Expectation Maximization Linear Discriminant Classifier"),
contains="LinearDiscriminantClassifier")
#' Semi-Supervised Linear Discriminant Analysis using Expectation Maximization
#'
#' Expectation Maximization applied to the linear discriminant classifier assuming Gaussian classes with a shared covariance matrix.
#'
#' Starting from the supervised solution, uses the Expectation Maximization algorithm (see Dempster et al. (1977)) to iteratively update the means and shared covariance of the classes (Maximization step) and updates the responsibilities for the unlabeled objects (Expectation step).
#'
#' @references Dempster, A., Laird, N. & Rubin, D., 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B, 39(1), pp.1-38.
#'
#' @param method character; Currently only "EM"
#' @param eps Stopping criterion for the maximinimization
#' @param verbose logical; Controls the verbosity of the output
#' @param max_iter integer; Maximum number of iterations
#' @inheritParams BaseClassifier
#' @family RSSL classifiers
#'
#' @export
EMLinearDiscriminantClassifier <- function(X, y, X_u, method="EM",scale=FALSE, eps=1e-8, verbose=FALSE, max_iter=100) {
## Preprocessing to correct datastructures and scaling
ModelVariables<-PreProcessing(X=X,y=y,X_u=X_u,scale=scale,intercept=FALSE)
X<-ModelVariables$X
X_u<-ModelVariables$X_u
y<-ModelVariables$y
scaling<-ModelVariables$scaling
classnames<-ModelVariables$classnames
modelform<-ModelVariables$modelform
Y <- model.matrix(~as.factor(y)-1)
Xe<-rbind(X,X_u)
if (method=="EM") {
responsibilities_old<-matrix(0,nrow(X_u),length(classnames)) # Set all posteriors to 0
g_iteration<-LinearDiscriminantClassifier(X,y)
responsibilities<-posterior(g_iteration,X_u) # Set posterior on the unlabeled objects based an classifier estimated on labeled objects
iteration <- 0
Ye<-rbind(Y,responsibilities)
logmarginal_old<-Inf
logmarginal <- losspart(g_iteration,Xe,Ye) #losslogsum(g_iteration,X,Y,X_u,responsibilities)
# print(logmarginal)
while (abs(logmarginal-logmarginal_old) > eps) {
iteration<- iteration+1
if (iteration>max_iter) { warning("Maximum number of iterations exceeded"); break }
prior<-matrix(colMeans(Ye),2,1)
means<-t((t(Xe) %*% Ye))/(colSums(Ye))
# sigma<-(sum(Ye[,1] * t(Xe-(matrix(1,nrow(Xe),1) %*% means[1,,drop=FALSE])) %*% (Xe-(matrix(1,nrow(Xe),1) %*% means[1,,drop=FALSE])))+sum(Ye[,2] * (Xe-(matrix(1,nrow(Xe),1) %*%means[2,,drop=FALSE]))^2))/(nrow(Xe)*ncol(Xe))
sigma <- (t(Xe-matrix(1,nrow(Ye),1) %*% means[1, ,drop=FALSE]) %*% diag(Ye[,1]) %*% (Xe-matrix(1,nrow(Ye),1) %*% means[1, ,drop=FALSE]) + t(Xe-matrix(1,nrow(Ye),1) %*% means[2, ,drop=FALSE]) %*% diag(Ye[,2]) %*% (Xe-matrix(1,nrow(Ye),1) %*% means[2, ,drop=FALSE]))/(nrow(Ye))
sigma<-lapply(1:ncol(Y),function(c){sigma})
g_iteration<-new("LinearDiscriminantClassifier", modelform=NULL, means=means, prior=prior, sigma=sigma,classnames=classnames,scaling=scaling)
if (verbose) cat("Loss after Parameter update: ",losspart(g_iteration,Xe,Ye),"\n")
responsibilities_old <- responsibilities
responsibilities<-posterior(g_iteration,X_u)
Ye<-rbind(Y,responsibilities)
logmarginal_old <- logmarginal
logmarginal <- losspart(g_iteration,Xe,Ye)
if (verbose) cat("Loss after Posterior update: ", losspart(g_iteration,Xe,Ye),"\n")
if (verbose) cat("Log of sum loss: ",losslogsum(g_iteration,X,Y,X_u,responsibilities),"\n")
}
}
new("EMLinearDiscriminantClassifier", modelform=modelform,
means=means, prior=prior, sigma=sigma,
classnames=classnames,scaling=scaling,
responsibilities=responsibilities)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.