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中的相应实体，已被广泛应用于各个领域。由于将要对齐的图通常来自不同的数据源，因此实际应用中结构和特征不一致的问题是无处不在的。大多数现有方法遵循“嵌入-交叉比较”的范例，即通过计算每个图中的节点嵌入并基于跨图嵌入比较处理节点对应。但是，我们发现当出现结构或特征不一致时，这些方法不稳定且次优。为此，我们提出了 SLOTAlign，一种无监督图对齐框架，联合执行结构学习和最优输运对齐。我们将图对齐转换为两个内部图矩阵之间的最优输运问题，无需跨图比较。我们进一步整合了多视角结构学习以增强图像表征能力并减少沿图传递的结构和特征不一致的影响。此外，已开发了一种基于交替方案的算法来解决 SLOTAlign 中的联合优化问题，并且还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和 DBP15K 知识图对齐基准数据集上进行了广泛实验。所提出的 SLOTAlign 表现出卓越的性能和最强的鲁棒性，优于七种无监督图对齐方法和五种专门的 KG 对齐方法。