Improved Graph Neural Network With Graph Filtering Kernel and Generalized Nonconvex Norm Inspired by a Novel Unified Optimization Framework

Graph neural network (GNN) is a powerful tool which has been achieving significant success via the prominent representation learning on the graph-structured data. However, due to the opaqueness of GNN, there has not yet been a unified framework for further guiding the designation and interpretation for GNN. Consequently, we first propose a novel unified optimization framework which can interpret most of the current GNN methods and give guidance for flexibly designing new GNN methods. It includes fitting item, global smooth item, and local smooth item. Motivated by our proposed unified optimization framework, an improved graph neural network with graph filtering kernel and generalized nonconvex norm (GFGN) is designed. In the GFGN model, we first introduce a novel graph filtering kernel for well alleviating the over-smoothing problem and getting more comprehensive information from original signals. At the same time, a generalized nonconvex norm for graph smoothing is also introduced, which can enhance the local smoothnesss adaptivity of graph for getting better robustness of GNN. Moreover, we adopt the predictor-corrector alternating gradient descent ascent (PCAGDA) algorithm to solve the proposed GFGN. At last, extensive experiments performed on benchmark datasets and adversarial datasets demonstrate the effectiveness and superiority of our proposed GFGN.