Graph neural networks with dual-stream cooperative learning of node and edge

Graph neural networks (GNNs) have assumed a pivotal role in advancing the domain of graph structure learning, particularly in undirected weighted graphs (UWGs). However, current GNNs typically utilize a single-node feature matrix to represent the nodes within UWGs, which may limit the learning capacity of the available feature space. Furthermore, sole dependence on neighborhood information may inadequately capture the intricate relationships, as edge features can encode implicit graph structure information and inherent dependencies among nodes. Motivated by these observations, this study proposes a Symmetry-preserving Dual-stream Node-Edge-joint-learning Graph Neural Network (SDNEG), which comprises two essential components: a) the dual-stream structure learning framework that can tolerate multiple node feature matrices, and b) the integration of a symmetry regularization term into the learning objective to enforce equality constraints on the multiple-node feature matrices, thereby highlighting the intrinsic symmetry of graphs and promoting joint learning of multiple-node embeddings. Quantitative findings from experiments conducted on two UWGs substantiate that the proposed SDNEG outperforms the baseline in missing weight estimation.