Mixup in Latent Geometry for Graph Classification

Mixup is a data augmentation method which can interpolate between existing data to create new samples. By enlarging the training distribution, it reduces the risk of over-fitting and improves generalization. Mixup is relatively straightforward to apply to image samples because pixels with equivalent coordinates in different images can be associated. However, alignment of distinct graphs with different sizes is non-trivial, thereby hindering the application of Mixup to graph data. Here we develop a novel algorithm to address this issue by exploiting the latent hyperbolic geometry which has been shown to underlie many real-world graphs. By considering global graph structure similarity and several fundamental structural features of graph models, we demonstrate that our mixup scheme leads to synthetic graphs whose structural features approximate the linear interpolation of parent graphs, a property important for avoiding the generation of mislabeled synthetic data. We apply the proposed algorithm to classify empirical graphs, and the results show that it improves classification performance on all six benchmark datasets and significantly enhances the generalization ability and robustness of graph neural networks.