A Novel Data Clustering Method Based on Smooth Non-negative Matrix Factorization
Non-negative matrix factorization (NMF) is a very popular dimensionality reduction method that has been widely used in computer vision and data clustering. However, NMF does not consider the intrinsic geometric information of a data set and also does not produce smooth and stable solutions. To resolve these problems, we propose a Graph regularized Lp Smooth Non-negative Matrix Factorization (GSNMF) method by incorporating graph regularization with Lp smooth constraint. The graph regularization can discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. The Lp smooth constraint can combine the merits of isotropic (L2-norm) and anisotropic (L1-norm) diffusion smoothing, and produce a smooth and more accurate solution to the optimization problem. Experimental results on some data sets demonstrate that the proposed method outperforms related state-of-the-art NMF methods.
KeywordsGraph regularization Smooth Non-negative Matrix Factorization (SNMF) Data clustering
This work is supported by the National Natural Science Foundation of China under Grant Nos. 61702251, 61363049, 11571011, 61501286, the State Scholarship Fund of China Scholarship Council (CSC) under Grant No. 201708360040, the Natural Science Foundation of Jiangxi Province under Grant No. 20161BAB212033, the Natural Science Basic Research Plan in Shaanxi Province of China under Program No. 2018JM6030, the Key Research and Development Program in Shaanxi Province of China under Grant No. 2018GY-008, the Doctor Scientific Research Starting Foundation of Northwest University under Grant No. 338050050 and Youth Academic Talent Support Program of Northwest University.
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