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

[Markus Metz]

Nikos Alexandris wrote:
>
> The thing is by multiplying by 0.0001 thing are worse concerning the
> *eigenvalues* (the eigenvectors are the same):
>
>
> # using the MODIS bands as they are
> r.info -r mod_b2
>
> min=0
> max=5504
>
>
> # use of i.pca gives
> r.info -h pca_mod_b267.1
>
> [...]
> Data Description:
>    generated by i.pca
> Comments:
>    Eigen values, (vectors), and [percent importance]:
>    PC1 6307563.04 (-0.6353,-0.6485,-0.4192)[98.71%]
>    PC2  78023.63 (-0.7124, 0.2828, 0.6422)[1.22%]
>    PC3   4504.60 (-0.2979, 0.7067,-0.6417)[0.07%]
>    
>
> # using MODIS bands multiplied by 0.0001
> r.info -r mod_b2_x
>
> min=0
> max=0.5504
>
>
> # using i.pca gives
> r.info -h pca.mod_x.1
>
> [...]   
> Data Description:
>    generated by i.pca
> Comments:
>    Eigen values, (vectors), and [percent importance]:
>    PC1      0.06 (-0.6353,-0.6485,-0.4192)[98.71%]
>    PC2      0.00 (-0.7124, 0.2828, 0.6422)[1.22%]
>    PC3      0.00 (-0.2979, 0.7067,-0.6417)[0.07%]
>
>   
OK, I don't have the full discussion on i.pca in my head, so I don't 
know how much sense my comments make. The loadings and percentages 
explained variance are identical, that's good. The Eigenvalues are not, 
it seems they were calculated from unstandardised (raw) values. For 
imagery processing, that may be desired, for other applications AFAIK it 
is required that input variables variables (here different bands) are 
standardised first so they can be combined and principal components 
extracted. I'm more familiar with non-spatial PCA, so it's high time I 
read the manual of i.pca, and the new wiki page on it...