Dictionary Learning With Few Samples and Matrix Concentration.

Let A be an n x n matrix, X be an n x p matrix, and Y = AX. A challenging and important problem in data analysis, motivated by dictionary learning and other practical problems, is to recover both A and X, given Y. Under normal circumstances, it is clear that this problem is underdetermined. However, in the case, when X is sparse and random, Spielman et al. showed that one can recover both A and X ...