mixOmics (version 6.2.0)

block.splsda: N-integration and feature selection with Projection to Latent Structures models (PLS) with sparse Discriminant Analysis

Description

Integration of multiple data sets measured on the same samples or observations to classify a discrete outcome to classify a discrete outcome and select features from each data set, ie. N-integration with sparse Discriminant Analysis. The method is partly based on Generalised Canonical Correlation Analysis.

Usage

block.splsda(X,
Y,
indY,
ncomp = 2,
keepX.constraint,
keepX,
design,
scheme,
mode,
scale = TRUE,
bias,
init ,
tol = 1e-06,
verbose,
max.iter = 100,
near.zero.var = FALSE)

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

A factor or a class vector indicating the discrete outcome of each sample.

indY

To be supplied if Y is missing, indicates the position of the factor / class vector outcome in the list X

ncomp

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

keepX.constraint

A list of same length as X. Each entry indicates specific variables to be selected in each of the blocks of X for the first PLS-components. See details and example.

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.

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.

bias

boleean. A logical value for biaised or unbiaised estimator of the var/cov. Default = FALSE.

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.

verbose

if set to TRUE, reports progress on computing.

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.

Value

block.splsda returns an object of class "block.splsda", "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

keepX.constraint

list indicating which variables (indices) where constrained to be used to build the first component for each block

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

weights

Correlation between the variate of each block and the variate of the outcome. Used to weight predictions.

explained_variance

Percentage of explained variance for each component and each block

Details

block.splsda function fits a horizontal integration PLS-DA model with a specified number of components per block). A factor indicating the discrete outcome needs to be provided, either by Y or by its position indY in the list of blocks X.

X 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.Our experience has shown that the constraint tuning and models can substantially improve the performance of the methods (see also tune.block.splsda)

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

References

On multiple integration with sPLS-DA and 4 data blocks:

Singh A., Gautier B., Shannon C., Vacher M., Rohart F., Tebbutt S. and Le Cao K.A. (2016). DIABLO: multi omics integration for biomarker discovery. BioRxiv available here: http://biorxiv.org/content/early/2016/08/03/067611

On data integration:

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

Gunther O., Shin H., Ng R. T. , McMaster W. R., McManus B. M. , Keown P. A. , Tebbutt S.J. , Le Cao K-A. , (2014) Novel multivariate methods for integration of genomics and proteomics data: Applications in a kidney transplant rejection study, OMICS: A journal of integrative biology, 18(11), 682-95.

mixOmics manuscript:

Rohart F, Gautier B, Singh A, Le Cao K-A. mixOmics: an R package for 'omics feature selection and multiple data integration. BioRxiv available here: http://biorxiv.org/content/early/2017/02/14/108597

See Also

plotIndiv, plotArrow, plotLoadings, plotVar, predict, perf, selectVar, block.plsda, block.spls and http://www.mixOmics.org/mixDIABLO for more details and examples.

Examples

# NOT RUN {
# block.splsda
# -------------
data("breast.TCGA")
# this is the X data as a list of mRNA, miRNA and proteins
data = list(mrna = breast.TCGA$data.train$mrna, mirna = breast.TCGA$data.train$mirna,
protein = breast.TCGA$data.train$protein)
# 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), protein = rep(10, 2))


TCGA.block.splsda = block.splsda(X = data, Y = breast.TCGA$data.train$subtype,
ncomp = ncomp, keepX = list.keepX, design = design)
TCGA.block.splsda

plotIndiv(TCGA.block.splsda, ind.names = FALSE)
# illustrates coefficient weights in each block
plotLoadings(TCGA.block.splsda, ncomp = 1, contrib = 'max')
plotVar(TCGA.block.splsda, style = 'graphics', legend = TRUE)


# block.splsda constraint
# -------------
# using the data and design from example above
## we force the first PLS-component of X to be built with only a few variables
# selected in the earlier example

constraint.mrna.comp1 = c("EPHB3", "CBR1", "BSPRY")
constraint.mirna.comp1  = c("hsa-mir-128-2", "hsa-mir-196b")
constraint.prot.comp1  = c("Paxillin")

TCGA.block.splsda.constraint = block.splsda(X = data, Y = breast.TCGA$data.train$subtype, ncomp = 2,
keepX = list(mrna = 20, mirna = 20, protein = 10),
keepX.constraint = list(mrna = list(constraint.mrna.comp1), mirna = list(constraint.mirna.comp1),
protein =  list(constraint.prot.comp1)))

# see if that subset contraint on comp 1 affected the variables selected in comp 2:
intersect(selectVar(TCGA.block.splsda.constraint, comp = 2)$mrna$name,
selectVar(TCGA.block.splsda, comp = 2)$mrna$name)

# indices of the constraint variables on the first component
TCGA.block.splsda.constraint$keepX.constraint
# }