Hierarchical Multi-Marginal Optimal Transport for Network Alignment

• URL: http://arxiv.org/abs/2310.04470v2
• Date: Sat, 10 Feb 2024 18:15:46 GMT
• Title: Hierarchical Multi-Marginal Optimal Transport for Network Alignment
• Authors: Zhichen Zeng, Boxin Du, Si Zhang, Yinglong Xia, Zhining Liu, Hanghang Tong
• Abstract summary: Multi-network alignment is an essential prerequisite for joint learning on multiple networks. We propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. Our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability.
• Score: 52.206006379563306
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network alignment is sparse due to the exponentially growing solution space and lack of high-order discrepancy measures. To fill this gap, we propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. To handle the large solution space, multiple networks are decomposed into smaller aligned clusters via the fused Gromov-Wasserstein (FGW) barycenter. To depict high-order relationships across multiple networks, the FGW distance is generalized to the multi-marginal setting, based on which networks can be aligned jointly. A fast proximal point method is further developed with guaranteed convergence to a local optimum. Extensive experiments and analysis show that our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability.

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