sipca: Independent Principal Component Analysis
In mixOmics: Omics Data Integration Project

Description Usage Arguments Details Value Author(s) References See Also Examples

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

sipca(
  X,
  ncomp = 3,
  mode = c("deflation", "parallel"),
  fun = c("logcosh", "exp"),
  scale = FALSE,
  max.iter = 200,
  tol = 1e-04,
  keepX = rep(50, ncomp),
  w.init = NULL
)

`X`	a numeric matrix (or data frame).
`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, choose 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`	(Default=FALSE) Logical indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is `FALSE` for consistency with `prcomp` function, but in general scaling is advisable. Alternatively, a vector of length equal the number of columns of `X` can be supplied. The value is passed to `scale`.
`max.iter`	integer, the maximum number of iterations.
`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).

See Details of ipca.

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

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
`X`	the centered data matrix
`x`	the principal components (with sparse independent loadings)
`loadings`	the sparse independent loading vectors
`kurtosis`	the kurtosis measure of the independent loading vectors
`prop_expl_var`	Proportion of the explained variance of derived components, after setting possible missing values to zero.

Fangzhou Yao, Jeff Coquery, Francois Bartolo, Kim-Anh Lê Cao, Al J Abadi

Yao, F., Coquery, J. and Lê 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.

ipca, pca, plotIndiv, plotVar and http://www.mixOmics.org for more details.

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")

# variables representation
plotVar(sipca.res, cex = 2.5)

plotVar(sipca.res, rad.in = 0.5, cex = 2.5,style="3d")

## End(Not run)