An $L^{\infty} Version of Principal Component Analysis? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T17:20:06Z http://mathoverflow.net/feeds/question/103990 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103990/an-l-infty-version-of-principal-component-analysis An$L^{\infty} Version of Principal Component Analysis? floc 2012-08-05T02:26:26Z 2012-08-05T08:40:48Z <p>I have a $k$ by $n$ matrix $A$, with $k \ll n$. In case it helps, the $k$ rows are orthonormal.</p> <p>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.</p> <p>This seems to be a little bit similar to PCA, which essentially finds rows with maximal L^2 norm.</p> <p>Thanks for any suggestions/literature references.</p>