用曲率流方法改进超图聚类，更敏感捕捉大超边结构。
Hypergraph clustering using Ricci curvature: an edge transport perspective
- 通过边上的概率传输定义超图曲率流
- 相比团扩张法对大超边更敏感，提升聚类效果
- 适合需要可解释性的超图社区发现任务
本文提出一种将曲率流扩展至超图的新方法，通过在边上定义概率测度并进行线性展开上的传输，生成新的边权重，显著提升社区检测性能。与基于团扩张的曲率流方法相比，该方法对超图结构更具敏感性，尤其在存在大超边时表现更优。两种方法互为补充，共同构成一个强大且高度可解释的超图社区检测框架。
原文摘要 · Abstract (English)
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.
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