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Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning.

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Title: Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning.
Authors: Shi, Kehan1 (AUTHOR) kshi@cjlu.edu.cn, Burger, Martin2,3 (AUTHOR)
Source: Journal of Scientific Computing. Jun2025, Vol. 103 Issue 3, p1-17. 17p.
Abstract: Hypergraph learning with p-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due to the non-differentiability of the objective function and the non-uniqueness of the minimizer. We derive a hypergraph p-Laplacian equation from the subdifferential of the p-Laplacian regularization. A simplified equation that is mathematically well-posed and computationally efficient is proposed as an alternative. Numerical experiments verify that the simplified p-Laplacian equation suppresses spiky solutions in data interpolation and improves classification accuracy in semi-supervised learning. The remarkably low computational cost enables further applications. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Scientific Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning.
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  Data: <searchLink fieldCode="AR" term="%22Shi%2C+Kehan%22">Shi, Kehan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kshi@cjlu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Burger%2C+Martin%22">Burger, Martin</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Scientific+Computing%22">Journal of Scientific Computing</searchLink>. Jun2025, Vol. 103 Issue 3, p1-17. 17p.
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  Data: Hypergraph learning with p-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due to the non-differentiability of the objective function and the non-uniqueness of the minimizer. We derive a hypergraph p-Laplacian equation from the subdifferential of the p-Laplacian regularization. A simplified equation that is mathematically well-posed and computationally efficient is proposed as an alternative. Numerical experiments verify that the simplified p-Laplacian equation suppresses spiky solutions in data interpolation and improves classification accuracy in semi-supervised learning. The remarkably low computational cost enables further applications. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of Scientific Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10915-025-02908-y
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      – Code: eng
        Text: English
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      – TitleFull: Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning.
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            NameFull: Shi, Kehan
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            – D: 01
              M: 06
              Text: Jun2025
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              Y: 2025
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