Sparsity-constrained Graph Nonnegative Matrix Factorization for Clustering

Abstract

Graph nonnegative matrix factorization (GNMF) is superior for mining the intrinsic geometric structure embedded in high-dimensional data. As the sparsity of the factorized matrices is crucial for clustering, the l 0 norm is commonly used in the formulated optimization problem to enforce the sparseness which makes the problem NP-hard and discontinuous. In this paper, the sparse graph nonnegative matrix factorization (SGNMF) is formulated as a global optimization problem by using the sum of inverted Gaussian functions to approximate the l 0 norm, the multiplicative update rules are developed to solve the problem with guaranteed convergence. The superior performance of the proposed approach is substantiated by clustering tests on four public datasets.