Depth-based Subgraph Convolutional Neural Networks

This paper proposes a new graph convolutional neural architecture based on a depth-based representation of graph structure, called the depth-based subgraph convolutional neural networks (DS-CNNs), which integrates both the global topological and local connectivity structures within a graph. Our idea is to decompose a graph into a family of K-layer expansion subgraphs rooted at each vertex, and then a set of convolution filters are designed over these subgraphs to capture local connectivity structural information. Specifically, we commence by establishing a family of K-layer expansion subgraphs for each vertex of graph by mapping graph to tree procedures, which can provide global topological arrangement information contained within a graph. We then design a set of fixed-size convolution filters and integrate them with these subgraphs (depicted in Figure 1). The idea is to apply convolution filters sliding over the entire subgraphs of a vertex to extract the local features analogous to the standard convolution operation on grid data. In particular, the convolution operation captures the local structural information within the graph, and has the weight sharing property among different positions of subgraph; the pooling operation acts directly on the output of the preceding layer without any preprocessing scheme (e.g., clustering or other techniques). Experiments on three graph-structured datasets demonstrate that our model DS-CNNs are able to outperform six state-of-the-art methods at the task of node classification.