Re: A basic question on Canonical Correlation Analysis

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?

I'm not completely sure I understand your question, but my fingers want to type:

Think of simple correlations as canonical correlations with restrictions on the coefficients of the canonical variables (that is, all but one are 0). You can never do worse by removing the restrictions.
.

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