[R] Estimate "between-axes" vs "within-axes heterogeneity of multivariate matrices

Nikos Alexandris nik at nikosalexandris.net
Wed Dec 22 04:55:10 CET 2010


My question(s) in the end might be silly but I am no expert on this, so here 
it goes:

Noy-Meir (1973), Pielou (1984) and a few others have pointed to non-centered 
PCA being in some cases useful. They clearly explain that "it is the case" 
when multi-dimensional data display distinct clusters (which have zero, or 
near-zero, projections in some subset of the axes) and the task is (exactly) 
to separate this clusters among the principal components.

I have done my complete work using prcomp() and tested combinations of 
center=FALSE/TRUE and scale=FALSE/TRUE. I would like to now check this 
"between-axes" vs "within-axes" heterogeneity of my data and cross-check 
results with the various tested PCA-versions.

Is there any (official or custom) function available in R that could answer 
this question? Some relative/comparative (preferrable simple and intuitive) 
measure(s)? Something that would graphically perhaps give an indication 
without time-consuming clustering, sampling or whatsoever processing?

Even though the above mentoined authors mention some measure for the assymetry 
of the yielded compoenents ( uncentered -> unipolar, centered -> bipolar) I 
find the concept a bit hard to understand.

Isn't there a quick way (function) to just say (with numbers of plots of 
course) "well, it seems that the data are heterogenous looking at between-
axes" or  the other way around "it looks like the variables differ within, 
more than between"?

Apologies for repeating the same question (trying to understand the problem 
myself). Thank you, Nikos

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