Analysis of Semi-Supervised Learning on Hypergraphs

• URL: http://arxiv.org/abs/2510.25354v1
• Date: Wed, 29 Oct 2025 10:19:32 GMT
• Title: Analysis of Semi-Supervised Learning on Hypergraphs
• Authors: Adrien Weihs, Andrea Bertozzi, Matthew Thorpe,
• Abstract summary: We propose Higher-Order Hypergraph Learning (HOHL), which regularizes via powers of Laplacians from skeleton graphs for multiscale smoothness.<n>HOHL converges to a higher-order Sobolev seminorm. Empirically, it performs strongly on standard baselines.
• Score: 1.8297494098768168
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hypergraphs provide a natural framework for modeling higher-order interactions, yet their theoretical underpinnings in semi-supervised learning remain limited. We provide an asymptotic consistency analysis of variational learning on random geometric hypergraphs, precisely characterizing the conditions ensuring the well-posedness of hypergraph learning as well as showing convergence to a weighted $p$-Laplacian equation. Motivated by this, we propose Higher-Order Hypergraph Learning (HOHL), which regularizes via powers of Laplacians from skeleton graphs for multiscale smoothness. HOHL converges to a higher-order Sobolev seminorm. Empirically, it performs strongly on standard baselines.

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