R: Sparse Principal Components Analysis

spca {mixOmics} | R Documentation

## Sparse Principal Components Analysis

### Description

Performs a sparse principal components analysis to perform variable selection by using singular value decomposition.

### Usage

    spca(X, ncomp = 2, center = TRUE, scale = TRUE,
         keepX = rep(ncol(X),ncomp), max.iter = 500,
         tol = 1e-06, logratio = 'none',  # one of ('none','CLR')
         multilevel = NULL)

### Arguments

`X` | a numeric matrix (or data frame) which provides the data for the sparse principal components analysis.
`ncomp` | integer, the number of components to keep.
`center` | a logical value indicating whether the variables should be shifted to be zero centered. Alternatively, a vector of length equal the number of columns of `X` can be supplied. The value is passed to `scale`.
`scale` | a logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is `TRUE`. See details.
`max.iter` | integer, the maximum number of iterations to check convergence in each component.
`tol` | a positive real, the tolerance used in the iterative algorithm.
`keepX` | numeric vector of length ncomp, the number of variables to keep in loading vectors. By default all variables are kept in the model. See details.
`logratio` | one of ('none','CLR'). Specifies the log ratio transformation to deal with compositional values that may arise from specific normalisation in sequencing data. Default to 'none'
`multilevel` | sample information for multilevel decomposition for repeated measurements.

### Details

The calculation employs singular value decomposition of the (centered and scaled) data matrix and LASSO to generate sparsity on the loading vectors.

`scale= TRUE` is highly recommended as it will help obtaining orthogonal sparse loading vectors.

`keepX` is the number of variables to keep in loading vectors. The difference between number of columns of `X` and `keepX` is the degree of sparsity, which refers to the number of zeros in each loading vector.

Note that `spca` does not apply to the data matrix with missing values. The biplot function for `spca` is not available.

According to Filzmoser et al., a ILR log ratio transformation is more appropriate for PCA with compositional data. Both CLR and ILR are valid.

Logratio transform and multilevel analysis are performed sequentially as internal pre-processing step, through `logratio.transfo` and `withinVariation` respectively.

Logratio can only be applied if the data do not contain any 0 value (for count data, we thus advise the normalise raw data with a 1 offset). For ILR transformation and additional offset might be needed.

### Value

`spca` returns a list with class `"spca"` containing the following components:

`ncomp` | the number of components to keep in the calculation.
`varX` | the adjusted cumulative percentage of variances explained.
`keepX` | the number of variables kept in each loading vector.
`iter` | the number of iterations needed to reach convergence for each component.
`rotation` | the matrix containing the sparse loading vectors.
`x` | the matrix containing the principal components.

### Author(s)

Kim-Anh Lê Cao, Fangzhou Yao, Leigh Coonan

### References

Shen, H. and Huang, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis 99, 1015-1034.

### See Also

`pca` and http://www.mixOmics.org for more details.

### Examples

    data(liver.toxicity)
    spca.rat <- spca(liver.toxicity$gene, ncomp = 3, keepX = rep(50, 3))
    spca.rat

    ## variable representation
    plotVar(spca.rat, cex = 0.5)
    ## Not run: plotVar(spca.rat,style="3d")

    ## samples representation
    plotIndiv(spca.rat, ind.names = liver.toxicity$treatment[, 3],
              group = as.numeric(liver.toxicity$treatment[, 3]))
    ## Not run: plotIndiv(spca.rat, cex = 0.01,
            col = as.numeric(liver.toxicity$treatment[, 3]),style="3d")
    ## End(Not run)

    # example with multilevel decomposition and CLR log ratio transformation
    # ----------------
    ## Not run:
    data("diverse.16S")
    pca.res = pca(X = diverse.16S$data.TSS, ncomp = 5,
    logratio = 'CLR', multilevel = diverse.16S$sample)
    plot(pca.res)
    plotIndiv(pca.res, ind.names = FALSE, group = diverse.16S$bodysite, title = '16S diverse data',
    legend=TRUE)

    ## End(Not run)

[Package mixOmics version 6.3.2 Index]