Schatten Graph Neural Networks

Graph Neural Networks (GNNs) have been intensively studied in recent years because of their promising performance over graph-structural data and have provided assistance in many fields. Recalling recent works on graph neural networks, we found that imposing graph smoothing via Frobenius norm was proven to be effective in the architecture of graph neural networks from the standpoint of the graph signal processing. In this paper, we aim to model the graph smoothness of graph neural networks using a Schatten p-norm with p in the interval [1, 2) to characterize smoothness and propose a novel architecture called Schatten graph neural networks. This architecture stems from a primal-dual solution scheme for a graph signal denoising problem. There is difficulty in solving subproblems with respect to the Schatten p-norm. We propose a fixed point iteration scheme and prove that it tracks with the linear convergence rate with solid mathematical analysis. Extensive experiments demonstrate the effectiveness of the proposed architecture of graph neural networks and their robustness to the graph adversarial attacks.