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Doubt about CCA and PCA

Dear Francisco, 

CCA and PCA are quite different methods. CCA regresses your 'response' data onto a set of explanatory variables. This needs to invert the matrix of covariances of the predictors, which is only possible if n>p, where n is the number of observations and p the number of explanatory variables.

PCA is defined in any case. The ratio between n and p is then relevant only if you intend to infer principal axes / component of the population (as opposed to using the PA/PC as mere descriptors of the sample). I would recommend reading :
Joliffe, I. T. Principal Component Analysis Springer, 2004
which tackles the latter point very clearly.

Best regards,

Thibaut.
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Dr Thibaut JOMBART
MRC Centre for Outbreak Analysis and Modelling
Department of Infectious Disease Epidemiology
Imperial College - Faculty of Medicine
St Mary?s Campus
Norfolk Place
London W2 1PG
United Kingdom
Tel. : 0044 (0)20 7594 3658
t.jombart at imperial.ac.uk
http://www1.imperial.ac.uk/medicine/people/t.jombart/
http://adegenet.r-forge.r-project.org/