NCGNN: Node-Level Capsule Graph Neural Network for Semisupervised Classification.

Message passing has evolved as an effective tool for designing graph neural networks (GNNs). However, most existing methods for message passing simply sum or average all the neighboring features to update node representations. They are restricted by two problems: 1) lack of interpretability to identify node features significant to the prediction of GNNs and 2) feature overmixing that leads to the oversmoothing issue in capturing long-range dependencies and inability to handle graphs under heterophily or low homophily. In this article, we propose a node-level capsule graph neural network (NCGNN) to address these problems with an improved message passing scheme. Specifically, NCGNN represents nodes as groups of node-level capsules, in which each capsule extracts distinctive features of its corresponding node. For each node-level capsule, a novel dynamic routing procedure is developed to adaptively select appropriate capsules for aggregation from a subgraph identified by the designed graph filter. NCGNN aggregates only the advantageous capsules and restrains irrelevant messages to avoid overmixing features of interacting nodes. Therefore, it can relieve the oversmoothing issue and learn effective node representations over graphs with homophily or heterophily. Furthermore, our proposed message passing scheme is inherently interpretable and exempt from complex post hoc explanations, as the graph filter and the dynamic routing procedure identify a subset of node features that are most significant to the model prediction from the extracted subgraph. Extensive experiments on synthetic as well as real-world graphs demonstrate that NCGNN can well address the oversmoothing issue and produce better node representations for semisupervised node classification. It outperforms the state of the arts under both homophily and heterophily.