Graph regularized Lp smooth non-negative matrix factorization for data representation

This paper proposes a Graph regularized Lp smooth non-negative matrix factorization ( GSNMF ) method by incorporating graph regularization and Lp smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second, the Lp smoothing constraint is incorporated into NMF to combine the merits of isotropic ( L2-norm ) and anisotropic ( L1-norm ) diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.