Inter- and intra-hypergraph regularized nonnegative matrix factorization with hybrid constraints

Abstract

The accurate low rank representation of high-dimensional data learned by the manifold regularized nonnegative matrix factorization framework is effective in data clustering. In previous work, this work has mainly been solved in the way of similarity matrix induction. To further increase the efficacy of low-rank representations, we propose a novel semi-supervised non-negative matrix factorization (NMF) model in this study called inter- and intra-hypergraph regularized non-negative matrix factorization with hybrid constraints (IGNMFC). IGNMFC constructs intra-hypergraph regularization and intra-hypergraph regularization by hypergraph learning, which can precisely induce high-dimensional data to map toward low-dimensional. Moreover, hybrid constraints are introduced to improve the exclusivity and sparsity of low-dimensional representations, and the result accounts for the benefit of this method in learning distinguishable subspace representations. Finally, IGNMFC is transformed into an optimal problem and an efficient iteration rule is proposed. Experiments on several datasets demonstrate that the proposed method outperforms the state-of-the-art NMF algorithms, and can achieve at least 7.9%∼15% accuracy improvement in most cases.