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Volume 6 Issue 2
Mar.  2019

IEEE/CAA Journal of Automatica Sinica

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Chengcai Leng, Hai Zhang, Guorong Cai, Irene Cheng and Anup Basu, "Graph Regularized \begin{document}$L_p$\end{document} Smooth Non-negative Matrix Factorization for Data Representation," IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 584-595, Mar. 2019. doi: 10.1109/JAS.2019.1911417
Citation: Chengcai Leng, Hai Zhang, Guorong Cai, Irene Cheng and Anup Basu, "Graph Regularized \begin{document}$L_p$\end{document} Smooth Non-negative Matrix Factorization for Data Representation," IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 584-595, Mar. 2019. doi: 10.1109/JAS.2019.1911417

Graph Regularized $L_p$ Smooth Non-negative Matrix Factorization for Data Representation

doi: 10.1109/JAS.2019.1911417
Funds:

the National Natural Science Foundation of China 61702251

the National Natural Science Foundation of China 61363049

the National Natural Science Foundation of China 11571011

the State Scholarship Fund of China Scholarship Council (CSC) 201708360040

the Natural Science Foundation of Jiangxi Province 20161BAB212033

the Natural Science Basic Research Plan in Shaanxi Province of China 2018JM6030

the Doctor Scientific Research Starting Foundation of Northwest University 338050050

More Information
  • This paper proposes a Graph regularized $L_p$ smooth non-negative matrix factorization (GSNMF) method by incorporating graph regularization and $L_p$ 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 $L_p$ smoothing constraint is incorporated into NMF to combine the merits of isotropic ($L_{2}$-norm) and anisotropic ($L_{1}$-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.

     

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