An $L^{\infty} Version of Principal Component Analysis? I have a$k$by$n$matrix$A$, with$k \ll n$. In case it helps, the$k$rows are orthonormal. I'm interested in finding a$k$by$k$orthogonal matrix$M$so as to maximize the$L^{\infty}$norms of the rows of$MA$. This is a little imprecise, since it may not be possible to maximize all of them simultaneously. At the moment, my criterion is to maximize the weighted sums of these$L^{\infty}$norms by some weights$w_{1}, \ldots, w_{k}\$. All of these weights are fairly similar, so if it is easier, I would also be happy with maximizing the average.

This seems to be a little bit similar to PCA, which essentially finds rows with maximal L^2 norm.

Thanks for any suggestions/literature references.

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it's called "principal" which means (in latin) about: "the main", or: "the first" (in a hierarchy)(Can't edit the title) – Gottfried Helms Aug 5 '12 at 3:34
– Steve Huntsman Aug 5 '12 at 11:18
Thanks for the comment on multidimensional scaling. I can see that this question fits into that framework, but that framework is much broader (and seems to encompass many things we'd like to do, but which are not computationally feasible). Do you know if this particular question (or one similar to it) has been addressed? – floc Aug 5 '12 at 21:31