Graph data augmentation with Gromow-Wasserstein Barycenters

Graphs are ubiquitous in various fields, and deep learning methods have been successful applied in graph classification tasks. However, building large and diverse graph datasets for training can be expensive. While augmentation techniques exist for structured data like images or numerical data, the augmentation of graph data remains challenging. This is primarily due to the complex and non-Euclidean nature of graph data. In this paper, it has been proposed a novel augmentation strategy for graphs that operates in a non-Euclidean space. This approach leverages graphon estimation, which models the generative mechanism of networks sequences. Computational results demonstrate the effectiveness of the proposed augmentation framework in improving the performance of graph classification models. Additionally, using a non-Euclidean distance, specifically the Gromow-Wasserstein distance, results in better approximations of the graphon. This framework also provides a means to validate different graphon estimation approaches, particularly in real-world scenarios where the true graphon is unknown.