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Graph-Regularized, Sparsity-Constrained Non-Negative Matrix Factorization with Earth Mover’s Distance Metric

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  • Shunli Li

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
    College of Mathematics and Information Science, Guiyang University, Guiyang 550005, China)

  • Linzhang Lu

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
    School of Mathematical Sciences, Xiamen University, Xiamen 361005, China)

  • Qilong Liu

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

  • Zhen Chen

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

Abstract

Non-negative matrix factorization (NMF) is widely used as a powerful matrix factorization tool in data representation. However, the traditional NMF, measured by Euclidean distance or Kullback–Leibler distance, does not take into account the internal implied geometric information of the dataset and cannot measure the distance between samples as well as possible. To remedy the defects, in this paper, we propose the NMF method with Earth mover’s distance as a metric, for short GSNMF-EMD. It combines graph regularization and L 1 / 2 smooth constraints. The GSNMF-EMD method takes into account the intrinsic implied geometric information of the dataset and can produce more sparse and stable local solutions. Experiments on two specific image datasets showed that the proposed method outperforms related state-of-the-art methods.

Suggested Citation

  • Shunli Li & Linzhang Lu & Qilong Liu & Zhen Chen, 2023. "Graph-Regularized, Sparsity-Constrained Non-Negative Matrix Factorization with Earth Mover’s Distance Metric," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1894-:d:1125428
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    References listed on IDEAS

    as
    1. Chen, Zigang & Li, Lixiang & Peng, Haipeng & Liu, Yuhong & Yang, Yixian, 2018. "Attributed community mining using joint general non-negative matrix factorization with graph Laplacian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 324-335.
    2. Zhengwei Qu & Jingchuan Yang & Yansheng Lang & Yunjing Wang & Xiaoming Han & Xinyue Guo, 2022. "Earth-Mover-Distance-Based Detection of False Data Injection Attacks in Smart Grids," Energies, MDPI, vol. 15(5), pages 1-16, February.
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