How to select k elements from two vectors of length n > k that maximize the correlation between the two vectors?

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Marco Brianti 2021-11-11

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https://ww2.mathworks.cn/matlabcentral/answers/1584599-how-to-select-k-elements-from-two-vectors-of-length-n-k-that-maximize-the-correlation-between-the

评论： Marco Brianti 2021-11-11

Hello everyone,

I have two numerical column vectors of length n, say vector A and vector B.

Consider a third column vector C which has k < n values equal to one, and zero otherwise.

I want C such that (A.*C)'*(B.*C) is maximized.

In other words, I need to decide which rows of A and B needs to remain (k of them needs to remain, n-k needs to me removed) to maximize the correlation between the vectors A and B. (In this sense, C can also be logical, 1 if row is in, zero if row is out)

Can you please help me to implement this maximization?

Many thanks for your help,

Marco

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Marco Brianti 2021-11-11

Dear John,

thanks for your reply. It is about the correlation. My point is that (A.*C)'*(B.*C) is somehow proportional to corr(A.*C,B.*C). Note that bewteen (A.*C)' and (B.*C) there is no dot-produc but only product. I am transposing the first vector such that the outcome is a scalar.

Does it make sense?

Many thanks,

Marco

Marco Brianti 2021-11-11