mixOmics (version 6.3.0)

block.spls: N-integration and feature selection with sparse Projection to Latent Structures models (sPLS)

Description

Integration of multiple data sets measured on the same samples or observations, with variable selection in each data set, ie. N-integration. The method is partly based on Generalised Canonical Correlation Analysis.

Usage

block.spls(X,
Y,
indY,
ncomp = 2,
keepX,
keepY,
design,
scheme,
mode,
scale = TRUE,
init ,
tol = 1e-06,
max.iter = 100,
near.zero.var = FALSE,
all.outputs = TRUE)

Arguments

X

A list of data sets (called 'blocks') measured on the same samples. Data in the list should be arranged in matrices, samples x variables, with samples order matching in all data sets.

Y

Matrix response for a multivariate regression framework. Data should be continuous variables (see block.splsda for supervised classification and factor reponse)

indY

To supply if Y is missing, indicates the position of the matrix response in the list X

ncomp

the number of components to include in the model. Default to 2. Applies to all blocks.

keepX

A list of same length as X. Each entry is the number of variables to select in each of the blocks of X for each component. In the case where keepX.constraint is specified it should indicate the number of variables to select on the remaining components. By default all variables are kept in the model.

keepY

Only if Y is provided. Each entry is the number of variables to select in each of the blocks of Y for each component. In the case where keepX.constraint is specified it should indicate the number of variables to select on the remaining components.

design

numeric matrix of size (number of blocks in X) x (number of blocks in X) with values between 0 and 1. Each value indicates the strenght of the relationship to be modelled between two blocks; a value of 0 indicates no relationship, 1 is the maximum value. If Y is provided instead of indY, the design matrix is changed to include relationships to Y.

scheme

Either "horst", "factorial" or "centroid". Default = horst, see reference.

mode

character string. What type of algorithm to use, (partially) matching one of "regression", "canonical", "invariant" or "classic". See Details. Default = regression.

scale

boleean. If scale = TRUE, each block is standardized to zero means and unit variances. Default = TRUE.

init

Mode of initialization use in the algorithm, either by Singular Value Decompostion of the product of each block of X with Y ("svd") or each block independently ("svd.single"). Default = svd.single.

tol

Convergence stopping value.

max.iter

integer, the maximum number of iterations.

near.zero.var

boolean, see the internal nearZeroVar function (should be set to TRUE in particular for data with many zero values). Default = FALSE.

all.outputs

boolean. Computation can be faster when some specific (and non-essential) outputs are not calculated. Default = TRUE.

Value

block.spls returns an object of class "block.spls", a list that contains the following components:

X

the centered and standardized original predictor matrix.

indY

the position of the outcome Y in the output list X.

ncomp

the number of components included in the model for each block.

mode

the algorithm used to fit the model.

keepX

Number of variables used to build each component of each block

keepY

Number of variables used to build each component of Y

keepX.constraint

list indicating which variables (indices) where constrained to be used in the first components for each block in the X data set

keepY.constraint

list indicating which variables (indices) where constrained to be used in the first components for each block in the Y data set

variates

list containing the variates of each block of X.

loadings

list containing the estimated loadings for the variates.

names

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

nzv

list containing the zero- or near-zero predictors information.

iter

Number of iterations of the algorthm for each component

explained_variance

Percentage of explained variance for each component and each block

Details

block.spls function fits a horizontal sPLS model with a specified number of components per block). An outcome needs to be provided, either by Y or by its position indY in the list of blocks X. Multi (continuous)response are supported. X and Y can contain missing values. Missing values are handled by being disregarded during the cross product computations in the algorithm block.pls without having to delete rows with missing data. Alternatively, missing data can be imputed prior using the nipals function.

The type of algorithm to use is specified with the mode argument. Four PLS algorithms are available: PLS regression ("regression"), PLS canonical analysis ("canonical"), redundancy analysis ("invariant") and the classical PLS algorithm ("classic") (see References and ?pls for more details).

Note that our method is partly based on sparse Generalised Canonical Correlation Analysis and differs from the MB-PLS approaches proposed by Kowalski et al., 1989, J Chemom 3(1), Westerhuis et al., 1998, J Chemom, 12(5) and sparse variants Li et al., 2012, Bioinformatics 28(19); Karaman et al (2014), Metabolomics, 11(2); Kawaguchi et al., 2017, Biostatistics.

Constraint model. To improve performance, a new argument was recently added to fit a constraint model (constraint=TRUE). The model is run on the optimal list of selected features keepX.constraint from the previous components, as opposed to considering only a specified number of features keepX.

Variable selection is performed on each component for each block of X, and for Y if specified, via input parameter keepX and keepY, and keepX.constraint and keepY.constraint for a constraint model. keepX.constraint and keepY.constraint specify variable names to be selected in the previous components of the model (see example).

Note that if Y is missing and indY is provided, then variable selection on Y is performed by specifying the input parameter directly in keepX.constraint and keepX (no keepY.constraint and keepY is needed).

References

Tenenhaus, M. (1998). La regression PLS: theorie 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.

Tenenhaus A. and Tenenhaus M., (2011), Regularized Generalized Canonical Correlation Analysis, Psychometrika, Vol. 76, Nr 2, pp 257-284.

Tenenhaus A., Philippe C., Guillemot V, Le Cao K.A., Grill J, Frouin V. Variable selection for generalized canonical correlation analysis. Biostatistics. kxu001

See Also

plotIndiv, plotArrow, plotLoadings, plotVar, predict, perf, selectVar, block.pls, block.splsda and http://www.mixOmics.org for more details.

Examples

# NOT RUN {
# Example with multi omics TCGA study
# -----------------------------
data("breast.TCGA")
# this is the X data as a list of mRNA and miRNA; the Y data set is a single data set of proteins
data = list(mrna = breast.TCGA$data.train$mrna, mirna = breast.TCGA$data.train$mirna)
# set up a full design where every block is connected
design = matrix(1, ncol = length(data), nrow = length(data),
dimnames = list(names(data), names(data)))
diag(design) =  0
design
# set number of component per data set
ncomp = c(2)
# set number of variables to select, per component and per data set (this is set arbitrarily)
list.keepX = list(mrna = rep(20, 2), mirna = rep(10,2))
list.keepY = c(rep(10, 2))

TCGA.block.spls = block.spls(X = data, Y = breast.TCGA$data.train$protein,
ncomp = ncomp, keepX = list.keepX, keepY = list.keepY, design = design)
TCGA.block.spls
# in plotindiv we color the samples per breast subtype group but the method is unsupervised!
plotIndiv(TCGA.block.spls, group =  breast.TCGA$data.train$subtype, ind.names = FALSE)
# illustrates coefficient weights in each block
plotLoadings(TCGA.block.spls, ncomp = 1)
plotVar(TCGA.block.spls, style = 'graphics', legend = TRUE)
network(TCGA.block.spls)

# }