Higher-order Weighted Graph Convolutional Networks

Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which suffers performance drop-off for deeper structure. Existing approaches that deal with the higher-order neighbors tend to take advantage of adjacency matrix power. In this paper, we assume a seemly trivial condition that the higher-order neighborhood information may be similar to that of the first-order neighbors. Accordingly, we present an unsupervised approach to describe such similarities and learn the weight matrices of higher-order neighbors automatically through Lasso that minimizes the feature loss between the first-order and higher-order neighbors, based on which we formulate the new convolutional filter for GCN to learn the better node representations. Our model, called higher-order weighted GCN(HWGCN), has achieved the state-of-the-art results on a number of node classification tasks over Cora, Citeseer and Pubmed datasets.