Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation
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 <inline-formula><math xmlns="http...
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MDPI AG
2023-06-01
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| author | Yunxia Xu Linzhang Lu Qilong Liu Zhen Chen |
| author_facet | Yunxia Xu Linzhang Lu Qilong Liu Zhen Chen |
| author_sort | Yunxia Xu |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> smooth nonnegative matrix factorization (HGSNMF) by incorporating the hypergraph regularization term and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-11T01:35:42Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:42Z |
| publishDate | 2023-06-01 |
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| spelling | doaj.art-ee7e427d130a4d75994f703433a108ac2023-11-18T17:01:50ZengMDPI AGMathematics2227-73902023-06-011113282110.3390/math11132821Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data RepresentationYunxia Xu0Linzhang Lu1Qilong Liu2Zhen Chen3School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaSchool of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaSchool of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaSchool of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, ChinaNonnegative 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> smooth nonnegative matrix factorization (HGSNMF) by incorporating the hypergraph regularization term and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/11/13/2821hypergraph regularization<i>L<sub>p</sub></i> smoothnonnegative matrix factorizationdata clustering |
| spellingShingle | Yunxia Xu Linzhang Lu Qilong Liu Zhen Chen Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation Mathematics hypergraph regularization <i>L<sub>p</sub></i> smooth nonnegative matrix factorization data clustering |
| title | Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation |
| title_full | Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation |
| title_fullStr | Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation |
| title_full_unstemmed | Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation |
| title_short | Hypergraph-Regularized <i>L</i><sub>p</sub> Smooth Nonnegative Matrix Factorization for Data Representation |
| title_sort | hypergraph regularized i l i sub p sub smooth nonnegative matrix factorization for data representation |
| topic | hypergraph regularization <i>L<sub>p</sub></i> smooth nonnegative matrix factorization data clustering |
| url | https://www.mdpi.com/2227-7390/11/13/2821 |
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