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Sparsity-constrained Graph Nonnegative Matrix Factorization for Clustering

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 l0 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 l0 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.