Nonnegative Matrix Factorization with Hypergraph Based on Discriminative Constraint and Nonsymmetric Reformulation

Nonnegative matrix factorization (NMF) is a widely used clustering method, which has been successfully applied to image clustering, community detection, text clustering, and other applications. However, NMF uses the linear combination of basis vectors, so when there is a nonlinear structure, NMF cannot find the combination of basis vectors representing the one cluster. Meanwhile, higher-order information among the nodes and the limited label information is often ignored. In this paper, we present a new model, namely NMF with hypergraph based on discriminative constraint and nonsymmetric reformulation (DNHNMF) to address this shortcoming. Specifically, DNHNMF formulates a symmetric matrix containing pairwise similarity values by reformulating the nonsymmetric matrix, explicitly combining label information and higher-order information, excavate the potential inherent cluster structure, and making the Euclidean distance between coefficient matrices (clustering assignment matrix) better represent the similarity measure among nodes. The clustering experiments of the proposed method are carried out and validated on eight standard datasets. Extensive experimental results show the effectiveness of the DNHNMF.