Dear All,

I am doing a simple correspondence analysis on a contingency table 
having more than 5000 lines (that are representing genes) and 4 columns. 
I am then doing a clustering analysis on the coordinates of all genes on 
the factorial axes. The results of the correspondence analysis are quite 
surprising to me. The coordinates of all rows on the 3 axes are strictly 
within a simplex that is a perfect tetrahedron. Of course, the 
extremities of the tetrahedron are corresponding to the coordinates of 
the column in the factorial space. How could such a structure be obtained?

I first thought that this was due to a specific structure in my original 
dataset, so I've decided to do the analysis again on a randomly drawn 
contingency table of the same size (each cell was drawn from a uniform 
distribution between 0 and 100). I collected again such a triangle 
structure.

It thus seems that a simple correspondence analysis is always producing 
such a triangular structure on a space with a small number of 
dimensions, but I never heard about this before. I suspect that people 
are usually not getting this because either they have more dimensions, 
or less rows in the original table, leading to points that look to be 
spread on factorial plans in a more homogeneous way.

Any explanation on this will be welcomed!

Eric

-- 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     Eric Wajnberg
     Chair of the ESF Scientific programme on
     Behavioural Ecology of Insect Parasitoids (BEPAR)
     Associated Professor at the UQAM
     (Universite du Quebec a Montreal)
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     Editor-in-Chief of BioControl, Published by Springer.

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