Enhancing robust semi-supervised graph alignment via adaptive optimal transport

The semi-supervised graph alignment problem aims to find the node correspondence across different graphs given a set of anchor links. Most existing methods employ the notion of alignment consistency or embedding-based techniques but overlook the global structure of graph data. Recently, an Optimal Transport (OT)-based method has been proposed for semi-supervised graph alignment by integrating structure-based embedding and OT distance, demonstrating its effectiveness in problem modeling. However, graphs to be aligned often exhibit significant structural differences, and a non-learnable transport cost design struggles to maintain generality when faced with such variations, especially in noisy real-world scenarios. Meanwhile, the challenge of efficiently incorporating anchor links into the cost design has not been thoroughly explored. In this paper, we propose RESAlign, a robust semi-supervised graph alignment framework that addresses the cross-domain alignment problem from both direct and indirect perspectives. By integrating multiple objective functions and an anchor-assisted heterogeneous graph learning module into the design of the transport cost, our framework adapts to structural differences across various graphs. Moreover, an additional weight-sharing mechanism is introduced to address node alignment from a distinct perspective, enabling effective generalization to unsupervised scenarios. Finally, compared to eleven representative methods, the proposed model not only achieves outstanding performance but also demonstrates excellent robustness and efficiency.