Algorithms for nonnegative matrix factorization with the beta-divergence

Understand

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF).

• The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito divergence as special cases (beta = 2,1,0, respectively).
• The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function).
• We first describe a majorization-minimization (MM) algorithm that leads to multiplicative updates, which differ from standard heuristic multiplicative updates by a beta-dependent power exponent.