factorization of matrices with unknown elements

been thinking about a problem that can be represented as a factorization (like svd or ica) of a matrix when only some of the elements are known. clearly not a simple problem, but one that apparently comes up in image recognition. google turned up an interesting report from oxford from 5 years ago that gives a good review of the problem. good descriptions of a few algorithms, observations on optimization methods (that may or may not carry over to other applications), and some synthetic examples that show the effect of the distribution of known elements. the residual function uses a hadamard (elementwise) product with a mask matrix to represent the partial knowledge, although sec 4.3 points out that other forms might better incorporate prior knowledge.