  A theoretical framework for non-negative matrix factorization based on
generalized dual Kullback-Leibler divergence, which includes members of the
exponential family of models, is proposed. A family of algorithms is developed
using this framework and its convergence proven using the
Expectation-Maximization algorithm. The proposed approach generalizes some
existing methods for different noise structures and contrasts with the recently
proposed quasi-likelihood approach, thus providing a useful alternative for
non-negative matrix factorizations. A measure to evaluate the goodness-of-fit
of the resulting factorization is described. This framework can be adapted to
include penalty, kernel and discriminant functions as well as tensors.
