Hierarchical Multi-Marginal Optimal Transport for Network Alignment

TL;DR

This paper introduces HOT, a hierarchical multi-marginal optimal transport framework for multi-network alignment, effectively handling large solution spaces and high-order relationships, with proven scalability and improved accuracy.

Contribution

The paper proposes a novel hierarchical multi-marginal optimal transport method using FGW barycenter decomposition for efficient multi-network alignment.

Findings

HOT outperforms existing methods in accuracy.

HOT demonstrates superior scalability.

The method effectively captures high-order network relationships.

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.