block.splsda {mixOmics} | R Documentation

## 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,
      design,
      scheme,
      scale = TRUE,
      init = "svd",
      tol = 1e-06,
      max.iter = 100,
      near.zero.var = FALSE,
      all.outputs = TRUE
    )

    wrapper.sgccda(
      X,
      Y,
      indY,
      ncomp = 2,
      keepX,
      design,
      scheme,
      scale = TRUE,
      init = "svd",
      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` | a factor or a class vector for the discrete outcome.
`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.
`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.
`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.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 `impute.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` if specified, via input parameter `keepX`.

### 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
`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
`weights` | Correlation between the variate of each block and the variate of the outcome. Used to weight predictions.
`prop_expl_var` | Percentage of explained variance for each component and each block

### Author(s)

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

### References

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

Singh A., Gautier B., Shannon C., Vacher M., Rohart F., Tebbutt S. and Lê 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, Lê 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. , Lê 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 article:

Rohart F, Gautier B, Singh A, Lê Cao K-A. mixOmics: an R package for 'omics feature selection and multiple data integration. PLoS Comput Biol 13(11): e1005752

### 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

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

    plotIndiv(TCGA.block.splsda, ind.names = FALSE)
    ## use design = 'null'
    TCGA.block.splsda = block.splsda(X = data, Y = breast.TCGA$data.train$subtype,
                                     ncomp = ncomp, keepX = list.keepX, design = 'null')
    TCGA.block.splsda$design
    ## set all off-diagonal elements to 0.5
    TCGA.block.splsda = block.splsda(X = data, Y = breast.TCGA$data.train$subtype,
                                     ncomp = ncomp, keepX = list.keepX, design = 0.5)
    TCGA.block.splsda$design
    # illustrates coefficient weights in each block
    plotLoadings(TCGA.block.splsda, ncomp = 1, contrib = 'max')
    plotVar(TCGA.block.splsda, style = 'graphics', legend = TRUE)

[Package mixOmics version 6.14.1 Index]