Perfect Clustering in Nonuniform Hypergraphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910909683728384 |
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| author | Chan, Ga-Ming Angus Lubberts, Zachary |
| author_facet | Chan, Ga-Ming Angus Lubberts, Zachary |
| contents | While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We introduce a hyper-edge-centric model for analyzing hypergraphs, called the interaction hypergraph, which models natural sampling methods for hypergraphs in neuroscience and communication networks, and accommodates interactions involving different numbers of entities. We define latent embeddings for the interactions in such a network, and analyze their estimators. In particular, we show that a spectral estimate of the interaction latent positions can achieve perfect clustering once enough interactions are observed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perfect Clustering in Nonuniform Hypergraphs Chan, Ga-Ming Angus Lubberts, Zachary Methodology Statistics Theory Machine Learning 05C65, 05C80, 60B20, 62F12 While there has been tremendous activity in the area of statistical network inference on graphs, hypergraphs have not enjoyed the same attention, on account of their relative complexity and the lack of tractable statistical models. We introduce a hyper-edge-centric model for analyzing hypergraphs, called the interaction hypergraph, which models natural sampling methods for hypergraphs in neuroscience and communication networks, and accommodates interactions involving different numbers of entities. We define latent embeddings for the interactions in such a network, and analyze their estimators. In particular, we show that a spectral estimate of the interaction latent positions can achieve perfect clustering once enough interactions are observed. |
| title | Perfect Clustering in Nonuniform Hypergraphs |
| topic | Methodology Statistics Theory Machine Learning 05C65, 05C80, 60B20, 62F12 |
| url | https://arxiv.org/abs/2504.08980 |