mixOmics (version 6.3.0)

spca: 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.

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.

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.

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

# NOT RUN {
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")
# }
# NOT RUN {
## 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")
# }
# 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)
# }