A novel framework for the NMF methods with experiments to unmixing signals and feature representation

Non-negative matrix factorization (NMF) can be used in clustering, feature representation or blind source separation. Many NMF methods have been developed including least squares (LS) error, Kullback–Leibler (KL) divergence, Itakura–Saito (IS) divergence, Bregman-divergence, α-divergence, β-divergence, γ-divergence, convex, constrained, graph-regularized NMFs. The main contribution of this paper is to develop a framework to generalize the existing NMF methods and also provide new NMF methods. This paper constructs a general optimization model and develops a generic updating rule with a simple structure using a surrogate function, which possesses similar properties as the standard NMF methods. The experimental results, obtained using several standard databases, demonstrate the power of the work in which some new methods provide performance superior to that of the other existing methods.