Analysis of Semi-Supervised Learning on Hypergraphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914169165447168 |
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| author | Weihs, Adrien Bertozzi, Andrea L. Thorpe, Matthew |
| author_facet | Weihs, Adrien Bertozzi, Andrea L. Thorpe, Matthew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of Semi-Supervised Learning on Hypergraphs Weihs, Adrien Bertozzi, Andrea L. Thorpe, Matthew Machine Learning Statistics Theory 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. |
| title | Analysis of Semi-Supervised Learning on Hypergraphs |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2510.25354 |