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Hypergraph Learning for Unsupervised Graph Alignment via Optimal Transport

AAAI 2025 · Graph learning › Graph self-supervised learning · approach: Semi-supervised node representation learning · 1 citations (OpenAlex)

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Proposes HLOT, which learns a weighted hypergraph via optimal transport with a Dirichlet-energy-inspired regularizer and combines graph and hypergraph structure/feature views in a Gromov-Wasserstein alignment for unsupervised graph alignment.

Problem

Unsupervised graph alignment finds node correspondences across graphs without ground-truth pairs, but pairwise graph edges miss higher-order relations among multiple nodes.

Approach

Learns a doubly stochastic hypergraph incidence matrix via entropic optimal transport with a hypergraph total-variation (Dirichlet energy) regularizer, then jointly uses graph and hypergraph structure and feature views as intra-graph metrics inside a Gromov-Wasserstein alignment with learned view weights.

Key results

• On Douban Online-Offline, HLOT reaches Hit@1 57.33 vs SLOTAlign 51.43, and Hit@30 87.12 vs 82.02 (reported 5.1% Hit@30 gain).
• On ACM-DBLP, HLOT Hit@1 is 65.94, slightly below SLOTAlign's 66.04, while Hit@30 is 91.32 vs 90.32.
• Under permutation and compression disturbances, HLOT attains best Hit@1 on most datasets, e.g., 99.56 on Cora permutation vs SLOTAlign 99.25.

Measured effects reported in the paper

Surprising findings

• Removing the graph structure view drops Douban Hit@1 from 57.33 to 1.07, showing graph structure is critical in this setup.
• On ACM-DBLP, HLOT's Hit@1 is marginally below SLOTAlign (65.94 vs 66.04).

Limitations

• Gains over SLOTAlign are modest on several datasets (e.g., ACM-DBLP Hit@1 is slightly lower).
• Hyperparameters tuned over grids and best Hit@k selected, which may favor the method.
• Hypergraph learning adds computation; complexity details deferred to appendix.

Experimental setup

Datasets: Douban Online-Offline ACM-DBLP Cora Citeseer PPI Facebook

Benchmarks: Douban Online-Offline ACM-DBLP Cora Citeseer PPI Facebook

Metrics: Hit@1 Hit@5 Hit@10 Hit@30

Baselines: KNN REGAL GCNAlign GATAlign WAlign GWD FusedGW SLOTAlign

Builds on: SLOTAlign Gromov-Wasserstein distance HGNN Hypergraph total variation

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