A framework for least squares nonnegative matrix factorizations with Tikhonov regularization

Abstract

Nonnegative matrix factorization (NMF) is widely used for dimensionality reduction, clustering and signal unmixing. This paper presents a generic model for least squares NMFs with Tikhonov regularization, which covers many well-known NMF models as well as new models. We also develop a generic updating rule with a simple structure to iteratively solve the optimization problem by constructing a surrogate function, which possesses properties similar to that of the standard NMF. The simulation results demonstrate the power of the framework in which some new algorithms can be derived to provide a performance superior to that of other commonly used methods.