Hierarchical Consistency Constraint for Robuster Unsupervised Graph Alignment

Unsupervised graph alignment aims to identify corresponding node pairs across two different graphs. Existing approaches typically utilize either structural or attribute information to obtain graph representation where intra-graph distances can be measured. However, the intertwined challenges of learning robust graph representations and effectively exploiting them for precise alignment remain key bottlenecks. To mitigate these issues, we propose a hierarchical consistency constraint (HCC) model that enforces hierarchical constraints on both the representation learning and alignment phases. Specifically, the graph distance consistency module works with a regularization term to learn representation robust to noise. For alignment, we propose the Karush–Kuhn–Tucker (KKT) consistency-enhanced Gromov-Wasserstein optimal transport (KGWOT) to ensure that the solution adheres to the KKT conditions during iterations. The KGWOT-based calculation module sparsifies the solution, leading to more accurate and robust alignment. Extensive experiments and analysis conducted on synthetic and real-world datasets demonstrate the robustness and accuracy of the proposed HCC model.