Saito, S;
Herbster, M;
(2022)
Generalizing p-Laplacian: spectral hypergraph theory and a partitioning algorithm.
Machine Learning
10.1007/s10994-022-06264-y.
(In press).
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Abstract
For hypergraph clustering, various methods have been proposed to defne hypergraph p-Laplacians in the literature. This work proposes a general framework for an abstract class of hypergraph p-Laplacians from a diferential-geometric view. This class includes previously proposed hypergraph p-Laplacians and also includes previously unstudied novel generalizations. For this abstract class, we extend current spectral theory by providing an extension of nodal domain theory for the eigenvectors of our hypergraph p-Laplacian. We use this nodal domain theory to provide bounds on the eigenvalues via a higher-order Cheeger inequality. Following our extension of spectral theory, we propose a novel hypergraph partitioning algorithm for our generalized p-Laplacian. Our empirical study shows that our algorithm outperforms spectral methods based on existing p-Laplacians.
| Type: | Article |
|---|---|
| Title: | Generalizing p-Laplacian: spectral hypergraph theory and a partitioning algorithm |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10994-022-06264-y |
| Publisher version: | https://doi.org/10.1007/s10994-022-06264-y |
| Language: | English |
| Additional information: | © 2022 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Spectral clustering, Hypergraph learning, Hypergraph pp-Laplacian, Cheeger inequality |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10161756 |
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