sPLS {sgPLS}

Sparse Partial Least Squares (sPLS)

Description

Function to perform sparse Partial Least Squares (sPLS). The sPLS approach combines both integration and variable selection simultaneously on two data sets in a one-step strategy.

Usage

sPLS(X, Y, ncomp, mode = "regression",
     max.iter = 500, tol = 1e-06, keepX = rep(ncol(X), ncomp), 
     keepY = rep(ncol(Y), ncomp),scale=TRUE)

Arguments

X

Numeric matrix of predictors.

Y

Numeric vector or matrix of responses (for multi-response models).

ncomp

The number of components to include in the model (see Details).

mode

Character string. What type of algorithm to use, (partially) matching one of "regression" or "canonical". See Details.

max.iter

Integer, the maximum number of iterations.

tol

A positive real, the tolerance used in the iterative algorithm.

keepX

Numeric vector of length ncomp, the number of variables to keep in X-loadings. By default all variables are kept in the model.

keepY

Numeric vector of length ncomp, the number of variables to keep in Y-loadings. By default all variables are kept in the model.

scale

a logical indicating if the orignal data set need to be scaled. By default scale=TRUE

Details

sPLS function fit sPLS models with 1, \ldots ,ncomp components. Multi-response models are fully supported.

The type of algorithm to use is specified with the mode argument. Two sPLS algorithms are available: sPLS regression ("regression") and sPLS canonical analysis ("canonical") (see References).

Value

sPLS returns an object of class "sPLS", a list that contains the following components:

X

The centered and standardized original predictor matrix.

Y

The centered and standardized original response vector or matrix.

ncomp

The number of components included in the model.

mode

The algorithm used to fit the model.

keepX

Number of X variables kept in the model on each component.

keepY

Number of Y variables kept in the model on each component.

mat.c

Matrix of coefficients to be used internally by predict.

variates

List containing the variates.

loadings

List containing the estimated loadings for the X and Y variates.

names

List containing the names to be used for individuals and variables.

tol

The tolerance used in the iterative algorithm, used for subsequent S3 methods

max.iter

The maximum number of iterations, used for subsequent S3 methods

Author(s)

Benoit Liquet and Pierre Lafaye de Micheaux.

References

Liquet Benoit, Lafaye de Micheaux Pierre, Hejblum Boris, Thiebaut Rodolphe. A group and Sparse Group Partial Least Square approach applied in Genomics context. Submitted.

Le Cao, K.-A., Martin, P.G.P., Robert-Grani\', C. and Besse, P. (2009). Sparse canonical methods for biological data integration: application to a cross-platform study. BMC Bioinformatics 10:34.

Le Cao, K.-A., Rossouw, D., Robert-Grani\'e, C. and Besse, P. (2008). A sparse PLS for variable selection when integrating Omics data. Statistical Applications in Genetics and Molecular Biology 7, article 35.

Shen, H. and Huang, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis 99, 1015-1034.

Tenenhaus, M. (1998). La r\'egression PLS: th\'eorie et pratique. Paris: Editions Technic.

Wold H. (1966). Estimation of principal components and related models by iterative least squares. In: Krishnaiah, P. R. (editors), Multivariate Analysis. Academic Press, N.Y., 391-420.

See Also

gPLS, sgPLS, predict, perf and functions from mixOmics package: summary, plotIndiv, plotVar, plot3dIndiv, plot3dVar.

Examples

## Simulation of datasets X and Y with group variables
n <- 100
sigma.gamma <- 1
sigma.e <- 1.5
p <- 400
q <- 500
theta.x1 <- c(rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5),
			rep(1.5, 15), rep(0, 5), rep(-1.5, 15), rep(0, 325))
theta.x2 <- c(rep(0, 320), rep(1, 15), rep(0, 5), rep(-1, 15),
			rep(0, 5), rep(1.5, 15), rep(0, 5), rep(-1.5, 15),
			rep(0, 5))

theta.y1 <- c(rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5), 
			rep(1.5, 15), rep(0, 5), rep(-1.5, 15), rep(0, 425))
theta.y2 <- c(rep(0, 420), rep(1, 15), rep(0, 5), rep(-1, 15)
			,rep(0, 5), rep(1.5, 15), rep(0, 5), rep(-1.5, 15)
			, rep(0, 5))                            


Sigmax <- matrix(0, nrow = p, ncol = p)
diag(Sigmax) <- sigma.e ^ 2
Sigmay <- matrix(0, nrow = q, ncol = q)
diag(Sigmay) <- sigma.e ^ 2

set.seed(125)

gam1 <- rnorm(n)
gam2 <- rnorm(n)

X <- matrix(c(gam1, gam2), ncol = 2, byrow = FALSE) %*% matrix(c(theta.x1, theta.x2),
     nrow = 2, byrow = TRUE) + rmvnorm(n, mean = rep(0, p), sigma =
     Sigmax, method = "svd")
Y <- matrix(c(gam1, gam2), ncol = 2, byrow = FALSE) %*% matrix(c(theta.y1, theta.y2),
     nrow = 2, byrow = TRUE) + rmvnorm(n, mean = rep(0, q), sigma =
     Sigmay, method = "svd")


ind.block.x <- seq(20, 380, 20)
ind.block.y <- seq(20, 480, 20)


#### sPLS model
model.sPLS <- sPLS(X, Y, ncomp = 2, mode = "regression", keepX = c(60, 60), 
                     keepY = c(60, 60))
result.sPLS <- select.spls(model.sPLS)
result.sPLS$select.X
result.sPLS$select.Y