R/fstep.qiao.R

In FisherEM: The FisherEM Algorithm to Simultaneously Cluster and Visualize High-Dimensional Data

fstep.qiao <- function(X,T,kernel){
	# Initialization
	K = ncol(T)
	p = ncol(X)
	d = min(p-1,(K-1))
	m = matrix(NA,K,p)

	# Compute summary statistics
	Xbar = colMeans(X)
	n = colSums(T)
	for (k in 1:K){ m[k,] = colSums((as.matrix(T[,k]) %*% matrix(1,1,p))* X) / n[k] }
# browser()	
	# Matrices Hb and Hw
	Hb =  as.matrix(sqrt(n) * (m - matrix(1,K,1) %*% Xbar))/sqrt(nrow(X))
	Hw = X - t(apply(T,1,'%*%',m))/sqrt(nrow(X))
	Hw = as.matrix(Hw)

	# Cholesky decomposition of t(Hw) %*% Hw
	if (nrow(X)>p)Rw = chol(t(Hw)%*%Hw) else {
		gamma = 0.5
		Rw = chol(t(Hw)%*%Hw + gamma*diag(p))}

	# LASSO & SVD
	Binit = eigen(ginv(cov(X))%*%(t(Hb)%*%Hb))$vect[,1:d]
	if (is.complex(Binit)) Binit = matrix(Re(Binit),ncol=d,byrow=F)
	if (is.null(dim(Binit))) {B = matrix(Binit)} else B = Binit
	res.svd = svd(t(ginv(Rw))%*%t(Hb)%*%Hb%*%B)
	A = res.svd$u %*% t(res.svd$v)	
# browser()
	for (j in 1:d){
		W = rbind(Hb,Rw)
		y = rbind(Hb %*% ginv(Rw) %*% A[,j],matrix(0,p,1))
# 		res.enet = enet(W,y,lambda=1,intercept=FALSE)
# 		B[,j] = predict.enet(res.enet,X,type="coefficients",mode="fraction",s=1)$coef
# browser()
		res.ls = lsfit(W,y,intercept=FALSE)
		B[,j]  = res.ls$coef
		}
	normtemp = sqrt(apply(B^2, 2, sum))                                                           
	normtemp[normtemp == 0] = 1
	Beta     = t(t(B)/normtemp)
	res.svd  = svd(t(ginv(Rw))%*%t(Hb)%*%Hb%*%Beta)
	A        = res.svd$u %*% t(res.svd$v)
	Beta     = svd(Beta)$u %*% t(svd(Beta)$v)
# 	Beta = svd(Beta)$u  
# 		Beta = qr.Q(qr(Beta))
	
	# return the sparse loadings
	Beta
}