Journal Article

PUBDB-2026-00500

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning

Shi, K. (Corresponding author) ; Burger, M.DESY*

2025
Springer Science + Business Media B.V. New York, NY [u.a.]

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Please use a persistent id in citations: doi:10.1007/s10915-025-02908-y  doi:10.3204/PUBDB-2026-00500

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.

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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Database coverage:
; ; Clarivate Analytics Master Journal List ; DEAL Springer ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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