For random geometric hypergraphs, the standard variational semi-supervised learning problem converges in the large-data limit to a density-weighted p-Laplacian problem, making it a first-order graph method; the proposed HOHL scheme converges to a higher-order Sobolev-type seminorm.
Consistency of fractional graph-Laplacian regularization in semisu- pervised learning with finite labels.SIAM Journal on Mathematical Analysis, 56(4):4253–4295, 2024
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Analysis of Semi-Supervised Learning on Hypergraphs
For random geometric hypergraphs, the standard variational semi-supervised learning problem converges in the large-data limit to a density-weighted p-Laplacian problem, making it a first-order graph method; the proposed HOHL scheme converges to a higher-order Sobolev-type seminorm.