rpls: Ridge Partial Least Square for binary 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 and Lambert-Lacroix (2005) RPLS algorithm.

1	rpls(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 {1,2}-valued vector and contains the response variable for each observation.
`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 rpls as a preliminary step before the algorithm is run.

The procedure described in Fort and Lambert-Lacroix (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) vector containing the coefficients weighting the 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 and S. Lambert-Lacroix (2005). Classification using Partial Least Squares with Penalized Logistic Regression, Bioinformatics, vol 21, n 8, 1104-1111.

rpls.cv, mrpls, mrpls.cv.

# load plsgenomics library
library(plsgenomics)

# load Colon data
data(Colon)
IndexLearn <- c(sample(which(Colon$Y==2),12),sample(which(Colon$Y==1),8))

# preprocess data
res <- preprocess(Xtrain= Colon$X[IndexLearn,], Xtest=Colon$X[-IndexLearn,],
                    Threshold = c(100,16000),Filtering=c(5,500),
                    log10.scale=TRUE,row.stand=TRUE)
# the results are given in res$pXtrain and res$pXtest

# perform prediction by RPLS
resrpls <- rpls(Ytrain=Colon$Y[IndexLearn],Xtrain=res$pXtrain,Lambda=0.6,ncomp=1,Xtest=res$pXtest)
resrpls$hatY
sum(resrpls$Ytest!=Colon$Y[-IndexLearn])

# prediction for another sample
Xnew <- res$pXtest[1,]
# Compute the linear predictor for each classes expect class 0
eta <- c(1,Xnew) %*% resrpls$Coefficients
Ypred <- which.max(c(0,eta))
Ypred