sPLS function

Sparse Partial Least Squares (sPLS)

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. latin1

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).

Returns

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

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.

Author(s)

Benoit Liquet and Pierre Lafaye de Micheaux.

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