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000644957 1001_ $$0P:(DE-HGF)0$$aShi, Kehan$$b0$$eCorresponding author
000644957 245__ $$aHypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning
000644957 260__ $$aNew York, NY [u.a.]$$bSpringer Science + Business Media B.V.$$c2025
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000644957 520__ $$aHypergraph learning with p-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due to the non-differentiability of the objective function and the non-uniqueness of the minimizer. We derive a hypergraph p-Laplacian equation from the subdifferential of the p-Laplacian regularization. A simplified equation that is mathematically well-posed and computationally efficient is proposed as an alternative. Numerical experiments verify that the simplified p-Laplacian equation suppresses spiky solutions in data interpolation and improves classification accuracy in semi-supervised learning. The remarkably low computational cost enables further applications.
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000644957 7001_ $$0P:(DE-H253)PIP1103953$$aBurger, Martin$$b1
000644957 773__ $$0PERI:(DE-600)2017260-6$$a10.1007/s10915-025-02908-y$$gVol. 103, no. 3, p. 93$$n3$$p93$$tJournal of scientific computing$$v103$$x0885-7474$$y2025
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