Graph regularized deep semi-nonnegative matrix factorization for clustering

Abstract

Matrix factorization technique has wide applications in data analysis, in which Semi-nonnegative Matrix Factorization (Semi-NMF) can learn an effective low-dimensional feature representation by semi-nonnegative limit inspired from cognition, and has a unique physical meaning that the whole is composed of the parts. In addition, the fashionable Deep Semi-NMF can learn more hidden information by deep factorization. But they do not consider the intrinsic geometric structure of complex data. However more effective feature representations can obtain by using the geometric structure information of complex data and local invariance. In this paper we regularize Semi-NMF and Deep Semi-NMF by using the neighbor graph for keeping the intrinsic geometric structure of the original data. So we propose two novel feature extracting algorithms: Graph Regularized Semi-NMF and Graph Regularized Deep Semi-NMF. The clustering experimental results on several benchmark datasets show that our Graph Regularized Semi-NMF and Graph Regularized Deep Semi-NMF outperform obviously Semi-NMF and Deep Semi-NMF respectively.