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Hypergraph-Regularized L p Smooth Nonnegative Matrix Factorization for Data Representation

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  • Yunxia Xu

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
    School of Science, Kaili University, Kaili 556011, 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

Nonnegative matrix factorization (NMF) has been shown to be a strong data representation technique, with applications in text mining, pattern recognition, image processing, clustering and other fields. In this paper, we propose a hypergraph-regularized L p smooth nonnegative matrix factorization (HGSNMF) by incorporating the hypergraph regularization term and the L p smoothing constraint term into the standard NMF model. The hypergraph regularization term can capture the intrinsic geometry structure of high dimension space data more comprehensively than simple graphs, and the L p smoothing constraint term may yield a smooth and more accurate solution to the optimization problem. The updating rules are given using multiplicative update techniques, and the convergence of the proposed method is theoretically investigated. The experimental results on five different data sets show that the proposed method has a better clustering effect than the related state-of-the-art methods in the vast majority of cases.

Suggested Citation

  • Yunxia Xu & Linzhang Lu & Qilong Liu & Zhen Chen, 2023. "Hypergraph-Regularized L p Smooth Nonnegative Matrix Factorization for Data Representation," Mathematics, MDPI, vol. 11(13), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2821-:d:1177744
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    References listed on IDEAS

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    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
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