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

[Nikos Alexandris]

Nikos:
> > The thing is by multiplying by 0.0001 thing are worse concerning the
> > *eigenvalues* (the eigenvectors are the same):

> > # use of i.pca gives
> > r.info -h pca_mod_b267.1
[...]
> >    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 i.pca gives
> > r.info -h pca.mod_x.1
[...]
> >    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%]


Markus M:   
> 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.

Yep.


> The Eigenvalues are not, it seems they were calculated from unstandardised (raw) values.

Note: the percent importance is nothing else than just transforemd
eigenvalues (that is: sum-up all eigenvalues and say the sum is the
100%, take then the percent of each eigenvalue).

The fact that the 2nd an d 3rd eigenvalues  in the above example are
0.00 is a (another) print-out/report issue I think.

However, the multiplication of the MODIS bands with the recommended
factor (0.0001) does nothing to the way i.pca treats the data.

##
I am convinced that i.pca wrongly _depends_ currently on the range of
the input data whether to apply data centering or not.

I just need to rescale the MODIS bands in to 0,255 and confirm my
skepsis. If I am wrong then it might be even more complicated!!
##


>  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. 

As Augustin Lobo and others suggested, data centering should be
performed. And me, with my limited knowledge and experience think the
same.


> 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...

Markus, I might missed to update some important sentences. So "handle
with care" :-)

Cheers, Nikos