A Cheeger cut for uniform hypergraphs
A Cheeger cut for uniform hypergraphs
The graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is bounded both above and below by the generalized Cheeger constant, and the corresponding eigenfunctions can be used to approximate the Cheeger cut.
Cheeger inequalities, Hypergraphs, Normalized Laplacian, Spectral clustering
2265-2286
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
5 June 2021
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Abstract
The graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is bounded both above and below by the generalized Cheeger constant, and the corresponding eigenfunctions can be used to approximate the Cheeger cut.
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2011.06816
- Accepted Manuscript
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Mulas2021_Article_ACheegerCutForUniformHypergrap
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2011.06816
- Accepted Manuscript
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Accepted/In Press date: 1 June 2021
e-pub ahead of print date: 5 June 2021
Published date: 5 June 2021
Keywords:
Cheeger inequalities, Hypergraphs, Normalized Laplacian, Spectral clustering
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Local EPrints ID: 449807
URI: http://eprints.soton.ac.uk/id/eprint/449807
ISSN: 0911-0119
PURE UUID: 7812d8a7-278f-495e-b84a-b25cf40e5f58
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Date deposited: 17 Jun 2021 16:36
Last modified: 16 Mar 2024 12:37
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Author:
Raffaella Mulas
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