Title: Unsupervised Multi-Scale Gromov-Wasserstein Hypergraph Alignment
Primary area: learning on graphs and other geometries & topologies
Keywords: Unsupervised hypergraph alignment, hypergraphs, Gromov-Wasserstein optimal transport, persistent homology

Abstract: We consider the problem of unsupervised hypergraph alignment, where the goal is to infer node correspondence between two hypergraphs based solely on their structure. Hypergraphs generalize graphs by allowing hyperedges to connect multiple nodes, and they provide a natural framework for modeling complex higher-order relationships. We introduce FALCON, a framework that effectively unifies hypergraph filtration with a multi-scale Gromov-Wasserstein consensus to solve unsupervised hypergraph alignment. The multi-scale, hierarchical structure revealed by filtration provides a set of robust, nested geometric constraints that are naturally regularized and aggregated by the GW framework. This synergy is uniquely suited to overcoming structural noise, a critical challenge where prior methods fail. Experiments on real-world datasets demonstrate that FALCON substantially outperforms state-of-the-art baselines, proving especially robust to noise.

TL;DR: We propose FALCON, a multi-scale Gromov–Wasserstein method that aligns hypergraphs without features by capturing higher-order structure and achieves robust, state-of-the-art performance.