Graph regularized Lp smooth non-negative matrix factorization for data representation
Chengcai Leng, Hai Zhang, Guorong Cai, Irene Cheng, Anup Basu · IEEE/CAA Journal of Automatica Sinica · 2019
This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization (GSNMF) method by incorporating graph regularization and Lpsmoothing 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 Lpsmoothing 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.