Non-negative Matrix Factorization: a Comprehensive Review

Non-negative matrix factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the non-negativity constraint and thus obtains the parts-based representation as well as enhancing the interpretability of the issue correspondingly. This survey paper mainly focuses on the theoretical research into NMF over the last five years, where the principles, basic models, properties, and algorithms of NMF along with its various modifications, extensions, and generalizations are summarized systematically. The existing NMF algorithms are divided into four categories: Basic NMF, Constrained NMF, Structured NMF, and Generalized NMF, upon which the design principles, characteristics, problems, relationships, and evolution of these algorithms are presented and analyzed comprehensively. Some related work not on NMF that NMF should learn from or has connections with is involved too. Moreover, some open issues remained to be solved are discussed. Several relevant application areas of NMF are also briefly described. This survey aims to construct an integrated, state-of-the-art framework for NMF concept, from which the follow-up research may benefit.