, Volume 51, Issue 1, pp 7-18

Nonnegative matrix factorization and its applications in pattern recognition

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Abstract

Matrix factorization is an effective tool for large-scale data processing and analysis. Nonnegative matrix factorization (NMF) method, which decomposes the nonnegative matrix into two nonnegative factor matrices, provides a new way for matrix factorization. NMF is significant in intelligent information processing and pattern recognition. This paper firstly introduces the basic idea of NMF and some new relevant methods. Then we discuss the loss functions and relevant algorithms of NMF in the framework of probabilistic models based on our researches, and the relationship between NMF and information processing of perceptual process. Finally, we make use of NMF to deal with some practical questions of pattern recognition and point out some open problems for NMF.