On Wed, 24 Feb 2016, Mike Stay wrote:
Say I've got a mxn matrix that I'd like to factor into an mxk and a kxn matrix. The factorization doesn't have to be exact; I'd just like to minimize some measure of error.
What are your favorite algorithms to do this? What assumptions about the matrix and the error measure do they make?
The usual way to do this is to take the singular value decomposition (SVD) and discard all but a few of the largest singular values (and the corresponding left and right singular vectors). This is the essence of "principal components analysis" (PCA). Makes no assumptions about the matrix. I'm not an expert, so I can't say what error measure this corresponds to. There's an enormous literature on PCA. Wikipedia appears to be very good on the subject. -- Tom Duff. In argento plane studiosus sum.