Hypergraph $p$-Laplacians and Scale Spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911863944511488 |
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| author | Fazeny, Ariane Tenbrinck, Daniel Lukin, Kseniia Burger, Martin |
| author_facet | Fazeny, Ariane Tenbrinck, Daniel Lukin, Kseniia Burger, Martin |
| contents | This paper introduces gradient, adjoint, and $p$-Laplacian definitions for oriented hypergraphs as well as differential and averaging operators for unoriented hypergraphs. These definitions are used to define gradient flows in the form of diffusion equations with applications in modelling group dynamics and information flow in social networks as well as performing local and non-local image processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15419 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hypergraph $p$-Laplacians and Scale Spaces Fazeny, Ariane Tenbrinck, Daniel Lukin, Kseniia Burger, Martin Social and Information Networks Combinatorics 05C65, 35R02, 91D30, 94A08 (Primary) 34L05, 35J05, 47B02, 91C20 (Secondary) This paper introduces gradient, adjoint, and $p$-Laplacian definitions for oriented hypergraphs as well as differential and averaging operators for unoriented hypergraphs. These definitions are used to define gradient flows in the form of diffusion equations with applications in modelling group dynamics and information flow in social networks as well as performing local and non-local image processing. |
| title | Hypergraph $p$-Laplacians and Scale Spaces |
| topic | Social and Information Networks Combinatorics 05C65, 35R02, 91D30, 94A08 (Primary) 34L05, 35J05, 47B02, 91C20 (Secondary) |
| url | https://arxiv.org/abs/2309.15419 |