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 feedback on the first submission of this work. In addition to minor changes (added references, appendix reorganisation, typos...), the paper has now undergone some significant revisions, most notably:

- The statement about the interpretability of the method has been properly justified (end of Section 4.2).
- After some close examination, the parameter alpha for the measure defined on edges had close to no impact at all. Indeed, pairs of nodes included in more than one hyperedge did not occur so often. Even when it occurred, changing alpha did not change anything in the transport plan at all. I assume that these edges belonging to both St(x) and St(y) were not transported at all. Hence, the measure on the edges has been modified to be parameter-free (Eq. 3)
-The measure on the nodes has been generalised to account for another parameter $p$ as done in Ni et al. This can significantly improve the accuracy. Figures and scores have been adapted accordingly.
-The main addition consists of a detailed ablation study of every hyperparameter. This corresponds to Section 4.3 and Appendix C. The initial claims regarding the fact that the hyperparameters play a small role in the final clustering accuracy were based on experiments on real datasets. However, on synthetic data, we examined some critical cases where changing the parameters can have a dramatic impact. I would like to thank the reviewers once more for their careful examination, as these aspects should not be overlooked.
-We provide an analysis of the trimming parameter $\tau$, where we compare the optimal value with the ones obtained by maximizing either the hypergraph modularity or the modularity of the clique graph. We found that it was always preferable to use the hypergraph modularity, and that it could have a dramatic impact on the results (See Table S5). This is not surprising, and is one more evidence that hypergraphs often call for hypergraph-specific tools.

Assigned Action Editor: ~Lorenzo_Orecchia1

Submission Number: 4953