mrpls: Ridge Partial Least Square for categorical data
In plsgenomics: PLS Analyses for Genomics

Description Usage Arguments Details Value Author(s) References See Also Examples

The function mrpls performs prediction using Fort et al. (2005) MRPLS algorithm.

1	mrpls(Ytrain,Xtrain,Lambda,ncomp,Xtest=NULL,NbIterMax=50)

`Xtrain`	a (ntrain x p) data matrix of predictors. `Xtrain` must be a matrix. Each row corresponds to an observation and each column to a predictor variable.
`Ytrain`	a ntrain vector of responses. `Ytrain` must be a vector. `Ytrain` is a {1,...,c+1}-valued vector and contains the response variable for each observation. c+1 is the number of classes.
`Xtest`	a (ntest x p) matrix containing the predictors for the test data set. `Xtest` may also be a vector of length p (corresponding to only one test observation).If `Xtest` is not equal to NULL, then the prediction step is made for these new predictor variables.
`Lambda`	a positive real value. `Lambda` is the ridge regularization parameter.
`ncomp`	a positive integer. `ncomp` is the number of PLS components. If `ncomp`=0,then the Ridge regression is performed without reduction dimension.
`NbIterMax`	a positive integer. `NbIterMax` is the maximal number of iterations in the Newton-Rapson parts.

The columns of the data matrices Xtrain and Xtest may not be standardized, since standardizing is performed by the function mrpls as a preliminary step before the algorithm is run.

The procedure described in Fort et al. (2005) is used to determine latent components to be used for classification and when Xtest is not equal to NULL, the procedure predicts the labels for these new predictor variables.

A list with the following components:

`Ytest`	the ntest vector containing the predicted labels for the observations from `Xtest`.
`Coefficients`	the (p+1) x c matrix containing the coefficients weighting the block design matrix.
`DeletedCol`	the vector containing the column number of `Xtrain` when the variance of the corresponding predictor variable is null. Otherwise `DeletedCol`=NULL
`hatY`	If `ncomp` is greater than 1, `hatY` is a matrix of size ntest x ncomp in such a way that the kth column corresponds to the predicted label obtained with k PLS components.

Sophie Lambert-Lacroix (http://membres-timc.imag.fr/Sophie.Lambert/).

G. Fort, S. Lambert-Lacroix and Julie Peyre (2005). Reduction de dimension dans les modeles lineaires generalises : application a la classification supervisee de donnees issues des biopuces. Journal de la SFDS, tome 146, n1-2, 117-152.

mrpls.cv, rpls, rpls.cv.

# load plsgenomics library
library(plsgenomics)

# load SRBCT data
data(SRBCT)
IndexLearn <- c(sample(which(SRBCT$Y==1),10),sample(which(SRBCT$Y==2),4),
			sample(which(SRBCT$Y==3),7),sample(which(SRBCT$Y==4),9))

# perform prediction by MRPLS
res <- mrpls(Ytrain=SRBCT$Y[IndexLearn],Xtrain=SRBCT$X[IndexLearn,],Lambda=0.001,ncomp=2,
			Xtest=SRBCT$X[-IndexLearn,])
sum(res$Ytest!=SRBCT$Y[-IndexLearn])

# prediction for another sample
Xnew <- SRBCT$X[83,]
# Compute the linear predictor for each classes expect class 1
eta <- diag(t(cbind(c(1,Xnew),c(1,Xnew),c(1,Xnew))) %*% res$Coefficients)
Ypred <- which.max(c(0,eta))
Ypred
SRBCT$Y[83]