Songyang Chen | Searcharxiv

arXiv2026

Towards Effective and Efficient Graph Alignment without Supervision

Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport (OT)-based approaches, we observe their limitations in terms of model accuracy-efficiency tradeoff. By focusing on the exploitation of local and global graph information, we formalize them as the ``local representation, global alignment'' paradigm, and present a new ``global representation and alignment'' paradigm to resolve the mismatch between the two phases in the alignment process. We then propose \underline{Gl}obal representation and \underline{o}ptimal transport-\underline{b}ased \underline{Align}ment (\texttt{GlobAlign}), and its variant, \texttt{GlobAlign-E}, for better \underline{E}fficiency. Our methods are equipped with the global attention mechanism and a hierarchical cross-graph transport cost, able to capture long-range and implicit node dependencies beyond the local graph structure. Furthermore, \texttt{GlobAlign-E} successfully closes the time complexity gap between representative embedding and OT-based methods, reducing OT's cubic complexity to quadratic terms. Through extensive experiments, our methods demonstrate superior performance, with up to a 20\% accuracy improvement over the best competitor. Meanwhile, \texttt{GlobAlign-E} achieves the best efficiency, with an order of magnitude speedup against existing OT-based methods.

cs.LG↗

arXiv2024

CombAlign: Enhancing Model Expressiveness in Unsupervised Graph Alignment

Unsupervised graph alignment finds the node correspondence between a pair of attributed graphs by only exploiting graph structure and node features. One category of recent studies first computes the node representation and then matches nodes with the largest embedding-based similarity, while the other category reduces the problem to optimal transport (OT) via Gromov-Wasserstein learning. However, it remains largely unexplored in the model expressiveness, as well as how theoretical expressivity impacts prediction accuracy. We investigate the model expressiveness from two aspects. First, we characterize the model's discriminative power in distinguishing matched and unmatched node pairs across two graphs. Second, we study the model's capability of guaranteeing node matching properties such as one-to-one matching and mutual alignment. Motivated by our theoretical analysis, we put forward a hybrid approach named CombAlign with stronger expressive power. Specifically, we enable cross-dimensional feature interaction for OT-based learning and propose an embedding-based method inspired by the Weisfeiler-Lehman test. We also apply non-uniform marginals obtained from the embedding-based modules to OT as priors for more expressiveness. Based on that, we propose a traditional algorithm-based refinement, which combines our OT and embedding-based predictions using the ensemble learning strategy and reduces the problem to maximum weight matching. With carefully designed edge weights, we ensure those matching properties and further enhance prediction accuracy. By extensive experiments, we demonstrate a significant improvement of 14.5% in alignment accuracy compared to state-of-the-art approaches and confirm the soundness of our theoretical analysis.

cs.LG↗