sipca: Independent Principal Component Analysis

Description

Performs sparse independent principal component analysis on the given data matrix to enable variable selection.

Usage

sipca(X, ncomp, mode = c("deflation","parallel"),
          fun = c("logcosh", "exp"),
          scale = FALSE, max.iter = 200,
          tol = 1e-04, keepX = rep(50,ncomp),
          w.init=NULL)

Arguments

a numeric matrix (or data frame) which provides the data for the principal component analysis.

ncomp

integer, number of independent component to choose. Set by default to 3.

mode

character string. What type of algorithm to use when estimating the unmixing matrix, (partially) matching one of "deflation", "parallel". Default set to deflation.

fun

the function used in approximation to neg-entropy in the FastICA algorithm. Default set to logcosh, see details of FastICA.

scale

a logical value indicating whether rows of the data matrix X should be standardized beforehand.

max.iter

integer, maximum number of iterations to perform.

tol

a positive scalar giving the tolerance at which the un-mixing matrix is considered to have converged, see fastICA package.

keepX

the number of variable to keep on each dimensions.

w.init

initial un-mixing matrix (unlike FastICA, this matrix is fixed here).

Value

pca returns a list with class "ipca" containing the following components:

ncomp

the number of principal components used.

unmixing

the unmixing matrix of size (ncomp x ncomp)

mixing

the mixing matrix of size (ncomp x ncomp

the centered data matrix

the principal components (with sparse independent loadings)

loadings

the sparse independent loading vectors

kurtosis

the kurtosis measure of the independent loading vectors

Details

See Details of ipca.

Soft thresholding is implemented on the independent loading vectors to obtain sparse loading vectors and enable variable selection.

References

Yao, F., Coquery, J. and L<U+00EA> Cao, K.-A. (2011) Principal component analysis with independent loadings: a combination of PCA and ICA. (in preparation)

A. Hyvarinen and E. Oja (2000) Independent Component Analysis: Algorithms and Applications, Neural Networks, 13(4-5):411-430

J L Marchini, C Heaton and B D Ripley (2010). fastICA: FastICA Algorithms to perform ICA and Projection Pursuit. R package version 1.1-13.

Examples

Run this code

# NOT RUN {
data(liver.toxicity)

# implement IPCA on a microarray dataset
sipca.res <- sipca(liver.toxicity$gene, ncomp = 3, mode="deflation", keepX=c(50,50,50))
sipca.res

# samples representation
plotIndiv(sipca.res, ind.names = liver.toxicity$treatment[, 4], 
          group = as.numeric(as.factor(liver.toxicity$treatment[, 4])))
# }
# NOT RUN {
plotIndiv(sipca.res, cex = 0.01,
            col = as.numeric(as.factor(liver.toxicity$treatment[, 4])),style="3d")
# }
# NOT RUN {
# variables representation
plotVar(sipca.res, cex = 2.5)
# }
# NOT RUN {
plotVar(sipca.res, rad.in = 0.5, cex = 2.5,style="3d")
# }

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