Non-negative matrix factorization based on generalized dual divergence

Nonnegative matrix factorization based on generalized dual divergence Karthik Devarajan Department of Biostatistics & Bioinformatics, Fox Chase Cancer Center, Temple University Health System, Philadelphia, PA karthik.devarajan@fccc.edu Keywords: nonnegative matrix factorization, Kullback-Leibler divergence, dual divergence, EM algorithm, high dimensional data, tensor Abstract A theoretical framework for nonnegative 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 nonnegative matrix factorizations. A measure to evaluate the goodness-of-fit of the resulting factorization is described.