Generative hypergraph models and spectral embedding
Abstract Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into low-dimensional Euclidean space so that most interactions...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-01-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-27565-9 |
| _version_ | 1797952537437929472 |
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| author | Xue Gong Desmond J. Higham Konstantinos Zygalakis |
| author_facet | Xue Gong Desmond J. Higham Konstantinos Zygalakis |
| author_sort | Xue Gong |
| collection | DOAJ |
| description | Abstract Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into low-dimensional Euclidean space so that most interactions are short-range. This embedding is relevant to many follow-on tasks, such as node reordering, clustering, and visualization. We focus on two spectral embedding algorithms customized to hypergraphs which recover linear and periodic structures respectively. In the periodic case, nodes are positioned on the unit circle. We show that the two spectral hypergraph embedding algorithms are associated with a new class of generative hypergraph models. These models generate hyperedges according to node positions in the embedded space and encourage short-range connections. They allow us to quantify the relative presence of periodic and linear structures in the data through maximum likelihood. They also improve the interpretability of node embedding and provide a metric for hyperedge prediction. We demonstrate the hypergraph embedding and follow-on tasks—including quantifying relative strength of structures, clustering and hyperedge prediction—on synthetic and real-world hypergraphs. We find that the hypergraph approach can outperform clustering algorithms that use only dyadic edges. We also compare several triadic edge prediction methods on high school and primary school contact hypergraphs where our algorithm improves upon benchmark methods when the amount of training data is limited. |
| first_indexed | 2024-04-10T22:47:57Z |
| format | Article |
| id | doaj.art-3066648f69054b7e9d1303ee41d013ab |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-10T22:47:57Z |
| publishDate | 2023-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-3066648f69054b7e9d1303ee41d013ab2023-01-15T12:11:25ZengNature PortfolioScientific Reports2045-23222023-01-0113111310.1038/s41598-023-27565-9Generative hypergraph models and spectral embeddingXue Gong0Desmond J. Higham1Konstantinos Zygalakis2School of Mathematics, University of EdinburghSchool of Mathematics, University of EdinburghSchool of Mathematics, University of EdinburghAbstract Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into low-dimensional Euclidean space so that most interactions are short-range. This embedding is relevant to many follow-on tasks, such as node reordering, clustering, and visualization. We focus on two spectral embedding algorithms customized to hypergraphs which recover linear and periodic structures respectively. In the periodic case, nodes are positioned on the unit circle. We show that the two spectral hypergraph embedding algorithms are associated with a new class of generative hypergraph models. These models generate hyperedges according to node positions in the embedded space and encourage short-range connections. They allow us to quantify the relative presence of periodic and linear structures in the data through maximum likelihood. They also improve the interpretability of node embedding and provide a metric for hyperedge prediction. We demonstrate the hypergraph embedding and follow-on tasks—including quantifying relative strength of structures, clustering and hyperedge prediction—on synthetic and real-world hypergraphs. We find that the hypergraph approach can outperform clustering algorithms that use only dyadic edges. We also compare several triadic edge prediction methods on high school and primary school contact hypergraphs where our algorithm improves upon benchmark methods when the amount of training data is limited.https://doi.org/10.1038/s41598-023-27565-9 |
| spellingShingle | Xue Gong Desmond J. Higham Konstantinos Zygalakis Generative hypergraph models and spectral embedding Scientific Reports |
| title | Generative hypergraph models and spectral embedding |
| title_full | Generative hypergraph models and spectral embedding |
| title_fullStr | Generative hypergraph models and spectral embedding |
| title_full_unstemmed | Generative hypergraph models and spectral embedding |
| title_short | Generative hypergraph models and spectral embedding |
| title_sort | generative hypergraph models and spectral embedding |
| url | https://doi.org/10.1038/s41598-023-27565-9 |
| work_keys_str_mv | AT xuegong generativehypergraphmodelsandspectralembedding AT desmondjhigham generativehypergraphmodelsandspectralembedding AT konstantinoszygalakis generativehypergraphmodelsandspectralembedding |