An Adaptive Neighborhood-Resonated Graph Convolution Network for Undirected Weighted Graph Representation

An undirected weighted graph (UWG) is the fundamental data representation in various real applications. A graph convolution network is frequently utilized for representation learning to a UWG. Nevertheless, existing graph convolutional networks (GCNs) only consider a node’s neighborhood during the embedding propagation, which regrettably decreases its representation learning capability due to the information loss in the modeling phase. Motivated by this discovery, this study proposes an adaptive neighborhood-resonated graph convolution network (ANR-GCN) with the following ideas: 1) establishing the weighted embedding propagation with the consideration of link weights in a UWG, thereby incorporating the interaction strength of each node pair into the ANR-GCN model; 2) building the neighborhood-regularization (NR) to make each node resonate with its neighborhoods, thus reinforcing the informative neighborhood information for improving the ANR-GCN’s representation capability to the complex topology of the target UWG; and 3)diversifying the NR effects following the attention principle for guaranteeing the ANR-GCN’s learning capacity. The proposed ANR-GCN’s representation learning ability to a UWG is theoretically guaranteed from the perspectives of bounded generalization error and uniform stability. Extensive experiments on four UWG datasets illustrate that the proposed ANR-GCN significantly outperforms state-of-the-art GCNs in missing edge detection in a UWG, which evidently demonstrates its superior performance.