Re: A basic question on Canonical Correlation Analysis

On 21 Nov 2005 14:23:01 -0800, gangxu_csu@xxxxxxxxx wrote:

> Hi, all,
>
> I have a basic question about canonical correlation.
>
> * put in the multivariate regression (multiple-input and
> multiple-output), and given some well-justified
> shrinkage/rank-reduction scheme, why would the canonical correlation
> give a better prediction to multiple-output than, e.g., simple
> correlations? Here simple correlation is one-variable to one-variable
> correlation. Which theoretical arguments do specifically support this
> statement?

Who uses a "shrinkage/rank-reduction scheme"?

The most-used version of canonical correlation is
the special case that is known as multiple-group
discriminant function. I don't see how your question(s)
or description has much traction. - Why does anybody
look at multiple groups instead of dichotomies? - Why
does anybody look at multiple predictors instead of one?


>
> * to further elaborate my question, e.g., I have N-input and N-output,
> I can perform CCA on observed data to establish canonical variate pairs
> and canonical correlation coefficients. Then I can apply some rank
> reduction scheme in CCA space. Finally, I apply rank-reduced (in CCA
> space) regression to some testing input data, to predict outputs. The
> other way would be applying simpler correlations to fit some models
> (say, multiple-regression models with each single-output as the
> reponse, neglecting correlations among output variables). If I don't
> actually go ahead to compare testing results between these two
> approaches, by what (theoretical) criteria, I can somehow analyze and
> conclude that CCA does be able to predict better than simpler
> correlation approaches?
>
> Any references that discussed this? any hints? Thanks a lot in advance!

This sounds to me as if your professor has asked you to
"describe and justify the use of CC." The answer must be
"Extrapolate from the justification for multiple regression."

If you aren't expecting the variables to be interesting
in combination, then you shouldn't expect the analysis
to tell you anything new.

References. You might google for
< discriminant MANOVA canonical-correlation >

The first hits look relevant.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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