Loadings and scores from fastICA?

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 F?rstenberg-H?gg 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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