Graph data augmentation has shown superiority in enhancing generalizability and robustness of GNNs in graph-level classifications. However, existing methods primarily focus on the augmentation in the graph signal space and the graph structure space independently, neglecting the joint interaction between them. In this paper, we address this limitation by formulating the problem as an optimal transport problem that aims to find an optimal inter-graph node matching strategy considering the interactions between graph structures and signals. To solve this problem, we propose a novel graph mixup algorithm called FGWMixup, which seeks a midpoint of source graphs in the Fused Gromov-Wasserstein (FGW) metric space. To enhance the scalability of our method, we introduce a relaxed FGW solver that accelerates FGWMixup by improving the convergence rate from $\mathcal{O}(t^{-1})$ to $\mathcal{O}(t^{-2})$. Extensive experiments conducted on five datasets using both classic (MPNNs) and advanced (Graphormers) GNN backbones demonstrate that FGWMixup effectively improves the generalizability and robustness of GNNs. Codes are available at https://github.com/ArthurLeoM/FGWMixup.

翻译：图数据增强在提升图神经网络（GNN）于图级分类任务中的泛化能力与鲁棒性方面展现出显著优势。然而，现有方法主要独立关注图信号空间与图结构空间的增强，忽略了两者之间的联合交互作用。本文通过将该问题建模为一个最优传输问题来突破此局限，该问题旨在考虑图结构与信号交互作用的前提下，寻找最优的跨图节点匹配策略。为解决该问题，我们提出了一种新型图混合算法FGWMixup，该算法在融合Gromov-Wasserstein（FGW）度量空间中寻找源图的中间点。为增强方法的可扩展性，我们引入了一个松弛的FGW求解器，通过将收敛速率从$\mathcal{O}(t^{-1})$提升至$\mathcal{O}(t^{-2})$来加速FGWMixup。在五个数据集上使用经典（MPNNs）与先进（Graphormers）GNN骨干网络进行的大量实验表明，FGWMixup能够有效提升GNN的泛化能力与鲁棒性。代码见https://github.com/ArthurLeoM/FGWMixup。