Re: A basic question on Canonical Correlation Analysis

Gary -

I'm stuck with your criteria "correlates *better*". I think,
that's the crucial part.
CCA looks for correlations in two sets as joint vector-group,
where each vector group is assumed to be a set of orthogonal
components. In this sets the components are searched, which
make the highest correlation. It is comparable with the idea
to find the principal components in each set and correlate
the principal components pairwise (though not exactly the same).
So whether this is "correlating *better*" I don't know; it's
just that.

When I was fiddling with CCA I came to the point, that I was
unsatisfied with the restriction of having components forced
to equal a principal components concept, and thought, the
problem of finding components would be "*better*" solved, if
the found PCA-like components were rotated to simple structure,
(if there is such in the sets).

Thus a 2-step-procedere
(1) applying CCA to find canonical composites (similar to principal
components)

(2) applying further rotation to the main canonical composites
to model simple structure in the set (if it is present there)
and the dominant subspace

seems to be a better approach to me, and may correspond more to
your point to have some kind of correlations related to the
individual variables in the sets. (But I haven't seen (2) in
literature yet)

Just a 0.02$ remark; I'm not much experienced with CCA in general.

Gottfried Helms

.