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### rplsaux.R (2006-01)
###
### Ridge Partial Least square for binary data
### (procedure used in CV function)
###
### Copyright 2006-01 Sophie Lambert-Lacroix
###
###
### This file is part of the `plsgenomics' library for R and related languages.
### It is made available under the terms of the GNU General Public
### License, version 2, or at your option, any later version,
### incorporated herein by reference.
###
### This program is distributed in the hope that it will be
### useful, but WITHOUT ANY WARRANTY; without even the implied
### warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
### PURPOSE. See the GNU General Public License for more
### details.
###
### You should have received a copy of the GNU General Public
### License along with this program; if not, write to the Free
### Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
### MA 02111-1307, USA
rplsaux <- function (Ytrain,sXtrain,Lambda,ncomp,sXtest,NbIterMax=50)
{
## INPUT VARIABLES
#########################
## sXtrain : matrix ntrain x r
## train data matrix
## Ytrain : vector ntrain
## response variable {0,1}-valued vector
## sXtest : matrix ntest x r
## test data matrix
## Lambda : real
## value for the regularization parameter Lambda
## NbIterMax : positive integer
## maximal number of iteration in the WIRRLS part
## ncomp : maximal number of PLS components
## 0 = Ridge
## OUTPUT VARIABLES
##########################
## hatY : matrix of size ntest x ncomp in such a way
## that the kieme column corresponds to the result
## for ncomp=k
## Cvg : 1 if convergence in WIRRLS 0 otherwise
r <- dim(sXtrain)[2]
ntrain <- dim(sXtrain)[1]
if (is.vector(sXtest)==TRUE)
{sXtest <- matrix(sXtest,nrow=1)}
ntest <- dim(sXtest)[1]
## RUN RPLS IN THE REDUCED SPACE
########################################
fit <- wirrls(Y=Ytrain,Z=cbind(rep(1,ntrain),sXtrain),Lambda=Lambda,NbrIterMax=NbIterMax,WKernel=diag(rep(1,ntrain)))
if (fit$Cvg==1) {
if (ncomp==0) #Ridge procedure
{GAMMA <- fit$Coefficients}
if (ncomp!=0) {
#Compute Weight and pseudo variable
#Pseudovar = Eta + W^-1 Psi
Eta <- cbind(rep(1,ntrain),sXtrain)%*%fit$Coefficients
mu<-1/(1+exp(-Eta))
diagW <- mu*(1-mu)
W <- diag(c(diagW))
Psi <- Ytrain-mu
## Run PLS
# W-Center the sXtrain and pseudo variable
Sum=sum(diagW)
# Weighted centering of Pseudo variable
WMeanPseudoVar <- sum(W%*%Eta+Psi)/Sum
WCtrPsi <- Psi
WCtrEta <- Eta-c(WMeanPseudoVar)
# Weighted centering of sXtrain
WMeansXtrain <- t(diagW)%*%sXtrain/Sum
WCtrsXtrain <- sXtrain-rep(1,ntrain)%*%WMeansXtrain
#Initialize some variables
PsiAux <- diag(c(rep(1,r)))
E <- WCtrsXtrain
f1 <- WCtrEta
f2 <- WCtrPsi
Omega <- matrix(0,r,ncomp)
Scores <- matrix(0,ntrain,ncomp)
TildePsi <- matrix(0,r,ncomp)
Loadings <- matrix(0,r,ncomp)
qcoeff <- vector(ncomp,mode="numeric")
GAMMA <- matrix(0,nrow=(r+1),ncol=ncomp)
#WPLS loop
for (count in 1:ncomp)
{Omega[,count]<-t(E)%*%(W%*%f1+f2)
#Score vector
t<-E%*%Omega[,count]
c<-t(Omega[,count])%*%t(E)%*%W%*%E%*%Omega[,count]
Scores[,count]<-t
TildePsi[,count] <- PsiAux%*%Omega[,count]
#Deflation of X
Loadings[,count]<-t(t(t)%*%W%*%E)/c[1,1]
E<-E-t%*%t(Loadings[,count])
#Deflation of f1
qcoeff[count]<-t(W%*%f1+f2)%*%t/c[1,1]
f1 <- f1-qcoeff[count]*t
#Recursve definition of RMatrix
PsiAux<-PsiAux%*%(diag(c(rep(1,r)))-Omega[,count]%*%t(Loadings[,count]))
#Express regression coefficients w.r.t. the columns of [1 sX] for ncomp=count
if (count==1)
{GAMMA[-1,count] <- TildePsi[,1:count]%*%t(c(qcoeff[1:count]))}
if (count!=1)
{GAMMA[-1,count] <- TildePsi[,1:count]%*%qcoeff[1:count]}
GAMMA[1,count] <- WMeanPseudoVar-WMeansXtrain%*%GAMMA[-1,count]}
}
## CLASSIFICATION STEP
#######################
ETA <- cbind(rep(1,ntest),sXtest)%*%GAMMA
hatY <- (ETA>0)+0
}
## CONCLUDE
##############
Cvg <- fit$Cvg
if (Cvg==1)
{List <- list(Convergence=Cvg,hatY=hatY)}
if (Cvg==0)
{List <- list(Convergence=Cvg)}
return(List)
}
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