mlsanityData to 14 Oct 2026

Hypergraph clustering using Ricci curvature: an edge transport perspective

arXiv 2412.15695 ↗First posted 20 Dec 2024cs.LG cs.SI stat.MLcited by 1

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Abstract (arXiv)

In this paper, we introduce a novel method for extending Ricci flow to hypergraphs by defining probability measures on the edges and transporting them on the line expansion. This approach yields a new weighting on the edges, which proves particularly effective for community detection. We extensively compare this method with a similar notion of Ricci flow defined on the clique expansion, demonstrating its enhanced sensitivity to the hypergraph structure, especially in the presence of large hyperedges. The two methods are complementary and together form a powerful and highly interpretable framework for community detection in hypergraphs.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 30 of its 60 references that are in the map. First posted on arXiv 20 Dec 2024.

Builds on

30 of 60 references.

References · 30

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18 more
  1. 2020The why, how, and when of representations for complex systemscited by 23
  2. 2015Ricci Curvature of the Internet Topologycited by 22
  3. 2020Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansioncited by 22
  4. 2018Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approachcited by 21
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  6. 2020Hypergraph Random Walks, Laplacians, and Clusteringcited by 20
  7. 2023Curvature-based Clustering on Graphscited by 14
  8. 2023Euler Characteristic Tools For Topological Data Analysiscited by 13
  9. 2022More Recent Advances in (Hyper)Graph Partitioningcited by 12
  10. 2022Ollivier-Ricci Curvature for Hypergraphs: A Unified Frameworkcited by 12
  11. 2020Ollivier-Ricci curvature convergence in random geometric graphscited by 11
  12. 2021Hypergraph Co-Optimal Transport: Metric and Categorical Propertiescited by 10
  13. 2018Forman-Ricci Curvature for Hypergraphscited by 9
  14. 2022HashNWalk: Hash and Random Walk Based Anomaly Detection in Hyperedge Streamscited by 5
  15. 2024Non-Euclidean Mixture Model for Social Network Embeddingcited by 4
  16. 2024Modularity Based Community Detection in Hypergraphscited by 3
  17. 2021Topological Simplifications of Hypergraphscited by 2
  18. 2023FREIGHT: Fast Streaming Hypergraph Partitioningcited by 1

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  1. 2025A roadmap for curvature-based geometric data analysis and learningcited by 0