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.

1 2 3 4 5 |

`X` |
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 |

`fun` |
the function used in approximation to neg-entropy in the FastICA algorithm. Default set to |

`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). |

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 |

Fangzhou Yao and Jeff Coquery.

Yao, F., Coquery, J. and LĂȘ 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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
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")
## End(Not run)
# variables representation
plotVar(sipca.res, cex = 2.5)
## Not run:
plotVar(sipca.res, rad.in = 0.5, cex = 2.5,style="3d")
## End(Not run)
``` |

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