[R] Loadings and scores from fastICA?

[Tony Plate]

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: tplate at acm.org
> > To: joel_furstenberg_hagg at hotmail.com
> > CC: r-help at 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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