Non-negative Matrix Factorization based on γ-divergence

Non-negative Matrix Factorization (NMF) is a method of multivariate analysis which factorizes a non-negative matrix into two non-negative matrices. While conventional NMF algorithms use the Euclidian distance or the Kullback-Leibler divergence as cost functions, those methods fail to extract latent structure or interpretable information from the matrix when the target matrix is contaminated by noise. In this paper, we propose novel NMF algorithms based on the γ-divergence which is known to be robust, and investigate robustness of proposed methods with numerical experiments.