SPOT: Spectral Optimal Transport for Graph Domain Generalization

Graph neural networks (GNNs) have essentially taken over as the de facto model for learning graph-structured data. However, the majority of existing methods perform transductive learning in a known graph, which is unable to tackle abundant in-the-wild unseen graphs with potential domain shifts. Even worse, these graphs, accompanied by domain shifts on structural topology and node attributes, bring in vulnerable data bias and thus a huge drop in performance. To tackle this, we propose a novel GNN method named spectral optimal transport (SPOT) for effective domain generalization on graphs. Our method is motivated by the fact that the high-frequency graph spectrum is more likely to indicate domain differences. In particular, we formulate the structural augmentation as an optimal transport problem to retain low-frequency key knowledge and solve the problem using Sinkhorn-Knopp algorithm. In addition, we incorporate an adaptive perturbation strategy to deep features, where the direction of the additive noise is determined by the homophily degrees to maintain semantic properties. Accordingly, we meticulously construct a collection of real-world benchmark datasets to assess the domain generalization capability of our model on graphs, and extensive experiments confirm the effectiveness of our proposed SPOT.