Symmetric nonnegative matrix factorization: A systematic review

In recent years, symmetric non-negative matrix factorization (SNMF), a variant of non-negative matrix factorization (NMF), has emerged as a promising tool for data analysis. This paper mainly focuses on the theoretical idea, the basic model, the optimization method, and the variants of SNMF. The SNMF-related approaches can be generally classified into two main categories, Classic SNMFs and Extended SNMFs. The classic SNMFs contain Orthogonal SNMF, Sparse SNMF, Manifold structure based SNMF and Pairwise constraint based SNMF, besides, extended SNMFs include Self-supervised SNMF, MV-WSNMF and Multi-view SNMF. According to different classes of SNMFs, this review elaborates on the key concepts, characteristics, and current issues of these algorithms. The clustering performance of SNMF and its variants on three object image datasets is empirically compared. In addition, the effects of some algorithms for solving SNMF have been compared and the performance of similarity matrix construction methods is also compared. Finally, some open problems with SNMF are discussed.