Robust graph convolutional networks with directional graph adversarial training

Graph convolutional networks (GCNs), an emerging type of neural network model on graphs, have presented state-of-the-art performance on the node classification task. However, recent studies show that neural networks are vulnerable to the small but deliberate perturbations on input features. And GCNs could be more sensitive to the perturbations since the perturbations from neighbor nodes exacerbate the impact on a target node through the convolution. Adversarial training (AT) is a regularization technique that has been shown capable of improving the robustness of the model against perturbations on image classification. However, directly adopting AT on GCNs is less effective since AT regards examples as independent of each other and does not consider the impact from connected examples. In this work, we explore AT on graph and propose a graph-specific AT method, Directional Graph Adversarial Training (DGAT), which incorporates the graph structure into the adversarial process and automatically identifies the impact of perturbations from neighbor nodes. Concretely, we consider the impact from the connected nodes to define the neighbor perturbation which restricts the perturbation direction on node features towards their neighbor nodes, and additionally introduce an adversarial regularizer to defend the worst-case perturbations. In this way, DGAT can resist the impact of worst-case adversarial perturbations and reduce the impact of perturbations from neighbor nodes. Extensive experiments demonstrate that DGAT can effectively improve the robustness and generalization performance of GCNs. Specially, GCNs with DGAT can provide better performance when there are rare few labels available for training.