| sgPLS {sgPLS} | R Documentation |
Sparse Group Partial Least Squares (sgPLS)
Description
Function to perform sparse group Partial Least Squares (sgPLS) in the conext of datasets are divided into groups of variables. The sgPLS approach enables selection at both groups and single feature levels.
Usage
sgPLS(X, Y, ncomp, mode = "regression",
max.iter = 500, tol = 1e-06, keepX,
keepY = NULL,ind.block.x, ind.block.y = NULL, alpha.x, alpha.y = NULL,
upper.lambda = 10 ^ 5,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 |
max.iter |
Integer, the maximum number of iterations. |
tol |
A positive real, the tolerance used in the iterative algorithm. |
keepX |
Numeric vector of length |
keepY |
Numeric vector of length |
ind.block.x |
A vector of integers describing the grouping of the |
ind.block.y |
A vector of integers describing the grouping of the |
alpha.x |
The mixing parameter (value between 0 and 1) related to the sparsity within group for the |
alpha.y |
The mixing parameter (value between 0 and 1) related to the sparsity within group for the |
upper.lambda |
By default |
scale |
a logical indicating if the orignal data set need to be scaled. By default |
Details
sgPLS function fit gPLS 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 gPLS
algorithms are available: gPLS regression ("regression") and gPLS canonical analysis
("canonical") (see References).
ind.block.x <- c(3, 10, 15) means that X is structured into 4 groups: X1 to X3; X4 to X10, X11 to X15 and X16 to Xp where p is the number of variables in the X matrix.
Value
sgPLS returns an object of class "sgPLS", 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 |
keepY |
Number of |
mat.c |
Matrix of coefficients to be used internally by |
variates |
List containing the variates. |
loadings |
List containing the estimated loadings for the |
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. |
iter |
Vector containing the number of iterations for convergence in each component. |
ind.block.x |
A vector of integers describing the grouping of the |
ind.block.y |
A vector of consecutive integers describing the grouping of the |
alpha.x |
The mixing parameter related to the sparsity within group for the |
alpha.y |
The mixing parameter related to the sparsity within group for the |
upper.lambda |
The upper bound of the intervall of lambda values for searching the value of the tuning parameter (lambda) corresponding to a non-zero group of variables. |
Author(s)
Benoit Liquet and Pierre Lafaye de Micheaux.
References
Liquet Benoit, Lafaye de Micheaux, Boris Hejblum, Rodolphe Thiebaut (2016). A group and Sparse Group Partial Least Square approach applied in Genomics context. Bioinformatics.
Le Cao, K.-A., Martin, P.G.P., Robert-Grani\'e, 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
sPLS, 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)
##
model.sgPLS <- sgPLS(X, Y, ncomp = 2, mode = "regression", keepX = c(4, 4),
keepY = c(4, 4), ind.block.x = ind.block.x
,ind.block.y = ind.block.y,
alpha.x = c(0.95, 0.95), alpha.y = c(0.95, 0.95))
result.sgPLS <- select.sgpls(model.sgPLS)
result.sgPLS$group.size.X
result.sgPLS$group.size.Y