Structured subspace learning-induced symmetric nonnegative matrix factorization

Symmetric NMF (SNMF) is able to determine the inherent cluster structure with the constructed graph. However, the mapping between the empirically constructed similarity representation and the desired one may contain complex structural and hierarchical information, which is not easy to capture with single learning approaches. Then, we propose a novel Structured Subspace Learning-induced Symmetric Nonnegative Matrix Factorization (SSLSNMF) in this paper. Based on the similarity space to be learned, SSLSNMF further learns a latent subspace, which considers the global and local structure of the data. Since SSLSNMF is formulated in a semi-supervised way, the supervisory information with constraints of cannot-link and must-link is also utilized. To guarantee that the latent similarity subspace to be discriminative, the global and local structures of the data as well as structural consistencies for limited labels in a semi-supervised manner are learned simultaneously in the proposed framework. An effective alternating iterative algorithm is proposed with proved convergence. Experiments conducted on six benchmark datasets show that better results can be obtained compared with state-of-the-art methods. (C) 2021 Elsevier B.V. All rights reserved.