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.

翻译：图对齐旨在识别多个网络间的对应实体，已被广泛应用于各个领域。由于待对齐的图通常来自不同数据源，在实际应用中，两个图之间的结构和特征不一致性问题普遍存在。现有方法大多遵循"先嵌入再交叉比较"的范式，即先计算每个图中的节点嵌入，再基于跨图嵌入比较处理节点对应关系。然而，我们发现当出现结构或特征不一致时，这些方法具有不稳定性且无法达到最优性能。为此，我们提出SLOTAlign——一种联合结构学习与最优传输对齐的无监督图对齐框架。我们将图对齐转化为两个图内矩阵之间的最优传输问题，无需跨图比较。我们进一步引入多视图结构学习以增强图表示能力，并降低图间继承的结构与特征不一致性的影响。此外，我们开发了基于交替方案的算法来解决SLOTAlign中的联合优化问题，并建立了可证明的收敛结果。最后，我们在六个无监督图对齐数据集及DBP15K知识图谱对齐基准数据集上进行了大量实验。与七种无监督图对齐方法和五种专用知识图谱对齐方法相比，所提出的SLOTAlign展现出卓越性能和最强鲁棒性。