Towards fidelity of graph data augmentation via equivariance

Graph data augmentation is widely used in machine learning, and when serving the underlying model, it is necessary to ensure that the feature–graph–label tuples are consistent before and after augmentation. To this end, controlling the fidelity of graph data augmentation to satisfy such consistency becomes a fundamental issue. To date, some graph data augmentation literature has discussed the importance of augmenting fidelity, but few theoretical guarantees have been provided. Here we theoretically ensure the fidelity by introducing the notion of aug-equivariance, based on its classical counterpart of equivariance. In our work, we first provide conditions to ensure that Graph Convolution Network is aug-equivariant with respect to the proposed transformations for both data and label distributions. Based on the derived conditions, we propose a novel graph data augmentation framework named E-Aug. The framework enables both edges and features to be augmented under the constraints of aug-equivariance, and the E-Aug-enhanced data does not damage the features and topology of the original graph. We experimentally applied E-Aug to various architectures such as Graph Convolutional Networks and Graph Attention Networks to verify the effectiveness of our method. Our E-Aug models can consistently improve or closely match state-of-the-art results across four established graph benchmarks:the Cora, Citeseer and Pubmed citation network datasets, as well as the Europe air traffic network dataset.