Loadings and scores from fastICA?

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
 		 	   		  

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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