Cauchy Graph Neural Networks

Graph Neural Networks (GNNs) have recently achieved remarkable success in graph representation and learning tasks. Many existing GNNs employ residual connection to effectively alleviate the over-smoothing issue in graph data learning. However, residual connection makes GNNs sensitive to abnormal node features with respect to feature noises and adversarial attacks. Furthermore, residual connection treats abnormal and normal nodes equally, which can lead to sub-optimal performance of GNNs. Therefore, developing a robust GNN is of great significance. In this work, we propose a novel Cauchy Graph Neural Network (CGNN) model, which leverages the Cauchy estimator from robust statistics to reduce the negative effects of abnormal nodes. Specifically, CGNN integrates the Cauchy estimator and graph Laplacian regularization into a unified framework. The core of CGNN is trying to adaptively assign small weights to abnormal nodes and large weights to normal nodes, thus improving the robustness of the model to abnormal node features. To implement CGNN, we devise an efficient optimization algorithm based on Half-Quadratic (HQ) theory and gradient descent. Experiments on several benchmark datasets demonstrate the robustness of the proposed method for different abnormal node feature scenarios.