Hierarchical Multi-Marginal Optimal Transport for Network Alignment
This work addresses the challenge of aligning multiple networks for joint learning, which is an incremental advancement over existing pair-wise alignment methods.
The paper tackles the problem of multi-network alignment, which involves finding node correspondence across multiple networks, by proposing a hierarchical multi-marginal optimal transport framework called HOT. The result shows that HOT achieves significant improvements in effectiveness and scalability over state-of-the-art methods, as demonstrated through extensive experiments.
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.