%0 Journal Article
%A Shi, Kehan
%A Burger, Martin
%T Hypergraph p-Laplacian Equations for Data Interpolation and Semi-supervised Learning
%J Journal of scientific computing
%V 103
%N 3
%@ 0885-7474
%C New York, NY [u.a.]
%I Springer Science + Business Media B.V.
%M PUBDB-2026-00500
%P 93
%D 2025
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%R 10.1007/s10915-025-02908-y
%U https://bib-pubdb1.desy.de/record/644957