Hypergraph clustering using Ricci curvature: an edge transport perspective

TMLR Paper4953 Authors

Abstract: 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.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=tbAZlUzlme&noteId=wtXea7Rox9

Changes Since Last Submission: I would like to thank the reviewers and the action editor for their thorough and very useful comments. The required modifications have been taken into account. The final modifications required by the action editor can be found at the end of Section 3.2.

Code: https://github.com/AnonRicciHG/Ricci_curv_HG

Assigned Action Editor: ~Lorenzo_Orecchia1

Submission Number: 4953