[GRASS-stats] Re: [GRASS-user] Testing i.pca ~ prcomp(), m.eigensystem ~ princomp()

[Nikos Alexandris]

On Wed, 2009-04-01 at 18:21 +0200, Edzer Pebesma wrote:
> Markus, a few notes:
> 
> - if you do PCA on uncentered data, by computing the eigenvalues of the
> uncentered covariance matrix, this implies that bands with a larger mean
> will get more influence on the final PCAs. I have sofar not managed
> finding an argument why this would be desirable.
> - if you do PCA on (band-mean)/sd(band), it means that you first
> normalize (scale) each variable to mean zero and unit variance. This
> procedure is identical to doing PCA on the correlation matrix. It means
> that, unlike for unscaled variables, variables with larger variance will
> not get more influence on the PCA than others. For image analysis I can
> see a place for both; if bands with low variance indicate insignificant
> and perhaps noisy information, you may downweight them. Or not, if they
> contain (equally) important information. Scaling becomes urgent when you
> compute PCAs from a mix of things with uncomparable units, such as image
> bands and DTMs.
> - Only in case of normalized variables, or equivalently PCA on
> correlations, it makes sense to select PC's with an eigenvalue larger
> than 1. The reasoning is fairly weak, but goes like this: if a PC has
> eigenvalue > 1, it explains more variance than any of the original
> variables, which all have variance 1.
> 
> Maybe I should Cc: this to the wiki.
> --
> Edzer

Nice to see this expert-comments! Really helpful to understand the
process better.

Thanks, Nikos