[R] Pointers to solutions to this PCA or Cononical Correlation type problem?

[LosemindL]

Hi all,

I am sure this is a well-studied stats problem, could anybody give me some
pointers?

It's similar to Canonical Correlation study.

We have a bunch of random variables, and want to figure out the set of
linear combinations of these variables, such that their mutual correlations
are all bounded by the upbound alpha. 

That's to say, giving n random variables x_1, ..., x_n, we want to obtain m
new random variables, 

y_1, y_2, ..., y_m, 

each one is a linear combination of the {x_1, ..., x_n},

and we want the max mutual correlation among {y_1, y_2, ..., y_m} to be
confined by an upbound alpha. 

Under that constraint, we would like to have m as large as possible.

Any "optimal" way of doing that? Or good engineering approach?

Thanks a lot!
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