sPLS: 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)

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

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

Author

Benoit Liquet and Pierre Lafaye de Micheaux.

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).

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.

Examples

Run this code


## 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

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