block.spls {mixOmics} | R Documentation

## 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 named 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 response).
`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 named 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. By default all variables are kept in the model.
`keepY` | Only if Y is provided (and not `indY`). Each entry is the number of variables to select in each of the blocks of Y for each component.
`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. Alternatively, one of c('null', 'full') indicating a disconnected or fully connected design, respecively, or a numeric between 0 and 1 which will designate all off-diagonal elements of a fully connected design (see examples in `block.splsda`). If `Y` is provided instead of `indY`, the `design` matrix is changed to include relationships to `Y`.
`scheme` | Character, one of 'horst', 'factorial' or 'centroid'. Default = `'horst'`, see reference.
`mode` | Character string indicating the type of PLS algorithm to use. One of `"regression"`, `"canonical"`, `"invariant"` or `"classic"`. See Details.
`scale` | Logical. 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 Decomposition of the product of each block of X with Y ('svd') or each block independently ('svd.single'). Default = `svd.single`.
`tol` | Positive numeric used as convergence criteria/tolerance during the iterative process. Default to `1e-06`.
`max.iter` | Integer, the maximum number of iterations. Default to 100.
`near.zero.var` | Logical, see the internal `nearZeroVar` function (should be set to TRUE in particular for data with many zero values). Setting this argument to FALSE (when appropriate) will speed up the computations. Default value is FALSE.
`all.outputs` | Logical. Computation can be faster when some specific (and non-essential) outputs are not calculated. Default = `TRUE`.

### 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.

Variable selection is performed on each component for each block of `X`, and for `Y` if specified, via input parameter `keepX` and `keepY`.

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` (no `keepY` is needed).

### 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
`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 algorithm for each component
`prop_expl_var` | Percentage of explained variance for each component and each block after setting possible missing values in the centered data to zero

### Author(s)

Florian Rohart, Benoit Gautier, Kim-Anh Lê Cao, Al J Abadi

### 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, Lê 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

    # 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)
    ## Not run:
    network(TCGA.block.spls)

    ## End(Not run)

[Package mixOmics version 6.16.3 Index]