Non-negative matrix factorization algorithms modeling noise distributions within the exponential family

We developed non-negative factorization algorithms based on statistical distributions which are members of the exponential family, and using multiplicative update rules. We compared in detail the performance of algorithms derived using two particular exponential family distributions, assuming either constant variance noise (Gaussian) or signal dependent noise (gamma). These algorithms were compared on both simulated data sets and on muscle activation patterns collected from behaving animals. We found that on muscle activation patterns, which are expected to be corrupted by signal dependent noise, the factorizations identified by the algorithm assuming gamma distributed data were more robust than those identified by the algorithm assuming Gaussian distributed data