Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport

TL;DR

SLOTAlign is an unsupervised framework for graph alignment that jointly learns structure and performs optimal transport-based alignment, demonstrating superior robustness and performance on multiple datasets.

Contribution

It introduces a novel joint structure learning and optimal transport approach for unsupervised graph alignment, addressing instability issues of existing methods.

Findings

Outperforms existing unsupervised graph alignment methods

Shows strong robustness across diverse datasets

Achieves state-of-the-art results on KG alignment benchmark

Abstract

Graph alignment, which aims at identifying corresponding entities across multiple networks, has been widely applied in various domains. As the graphs to be aligned are usually constructed from different sources, the inconsistency issues of structures and features between two graphs are ubiquitous in real-world applications. Most existing methods follow the ``embed-then-cross-compare'' paradigm, which computes node embeddings in each graph and then processes node correspondences based on cross-graph embedding comparison. However, we find these methods are unstable and sub-optimal when structure or feature inconsistency appears. To this end, we propose SLOTAlign, an unsupervised graph alignment framework that jointly performs Structure Learning and Optimal Transport Alignment. We convert graph alignment to an optimal transport problem between two intra-graph matrices without the requirement of cross-graph comparison. We further incorporate multi-view structure learning to enhance graph representation power and reduce the effect of structure and feature inconsistency inherited across graphs. Moreover, an alternating scheme based algorithm has been developed to address the joint optimization problem in SLOTAlign, and the provable convergence result is also established. Finally, we conduct extensive experiments on six unsupervised graph alignment datasets and the DBP15K knowledge graph (KG) alignment benchmark dataset. The proposed SLOTAlign shows superior performance and strongest robustness over seven unsupervised graph alignment methods and five specialized KG alignment methods.