Design of affinity-aware encoding by embedding graph centrality for graph classification

Abstract

Deep learning methods for graph classification are critical for graph data mining. Recently, graph convolutional networks (GCNs) have been able to achieve state-of-the-art node classification. A typical process for GCNs includes two iterative steps: node feature encoding and message passing. While the former encodes each graph node independently via the uniform encoding function, the latter updates the features of each node by weighted aggregation of the features of neighboring nodes, where the weights are generated by predefined or learned graph Laplacian. However, their accuracy deteriorates for graph classification tasks because the uniform encoding function encodes all the node features involved. In this study, we propose a novel affinity-aware encoding for graph classification. In our model, we implement a separate encoding function for the neighboring nodes of each node for updating the node features, where the nodes are arranged in the order of affinity values, such as graph centrality, in order to determine the correspondence between an encoding function and a specific neighboring node. Our separate encoding function performs non-Euclidean neighboring encoding for each node by weight sharing, which enables message passing. We also develop two variants based on our separate encoding function: the graph centrality-convolutional neural network (C-CNN) and the graph centrality-graph convolutional network (C-GCN). The former performs the separate encoding function on graph data directly by the function of message passing. The latter combines the separate encoding function with the normalized graph Laplacian implemented on the graph data. Experiments demonstrate that the results obtained by our models are consistent with those obtained by classical convolutional neural networks (CNNs) on the MNIST dataset, and they outperform existing GCNs on the 20NEWS, Reuters8, and Reuters52 datasets. We also apply our two variants to online car-hailing service data for traffic congestion recognition. Our methods show state-of-the-art results compared with GCNs.