ICA and PCA both model the data as a product of two matrices (usually
called something like components or loadings & weights or scores). It's
how those matrices are constructed that differs. PCA is often a first
step in doing ICA. I'd suggest reading the ICA tutorial by *Aapo
Hyvärinen and Erkki Oja *
(http://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/) -- it's an
excellent introduction.
-- Tony Plate
Joel Fürstenberg-Hägg wrote:
Ok, so then the S gives the individual components, good. Thanks Tony!
But what about the principal components from the PCA plot, how are
they calculated?
And are the linear mixing matrix A really the same as the
loadings/weights? There must be different loadings for the PCA and ICA
right?
Best regards,
Joel
> Date: Wed, 11 Nov 2009 14:29:06 -0700
> From: tpl...@acm.org
> To: joel_furstenberg_h...@hotmail.com
> CC: r-help@r-project.org
> Subject: Re: [R] Loadings and scores from fastICA?
>
> The help for fastICA says:
>
> The data matrix X is considered to be a linear combination of
> non-Gaussian (independent) components i.e. X = SA where columns of
> S contain the independent components and A is a linear mixing
> matrix.
>
> The value of fastICA is a list with components "S" (the estimated
source matrix) and "A" (the estimated mixing matrix). Are these what
you want?
>
> -- Tony Plate
>
> Joel Fürstenberg-Hägg wrote:
> > Hi all,
> >
> >
> >
> > Does anyone know how to get the independent components and
loadings from an Independent Component Analysis (ICA), as well as
principal components and loadings from a Pricipal Component analysis
(PCA) using the fastICA package? Or perhaps if there's another way to
do ICAs in R?
> >
> >
> > Below is an example from the fastICA manual
(http://cran.r-project.org/web/packages/fastICA/fastICA.pdf)
> >
> >
> >
> > if(require(MASS))
> > {
> > x <- mvrnorm(n = 1000, mu = c(0, 0), Sigma = matrix(c(10, 3, 3,
1), 2, 2))
> > x1 <- mvrnorm(n = 1000, mu = c(-1, 2), Sigma = matrix(c(10, 3, 3,
1), 2, 2))
> > X <- rbind(x, x1)
> > a <- fastICA(X, 2, alg.typ = "deflation", fun = "logcosh", alpha =
1, method = "R", row.norm = FALSE, maxit = 200, tol = 0.0001, verbose
= TRUE)
> > par(mfrow = c(1, 3))
> > plot(a$X, main = "Pre-processed data")
> > plot(a$X%*%a$K, main = "PCA components")
> > plot(a$S, main = "ICA components")
> > }
> >
> >
> >
> > Best regards,
> >
> >
> >
> > Joel
> >
> > _________________________________________________________________
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> >
> >
> >
> >
> >
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> >
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