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.
We propose HWGCN to mix the relevant neighborhood information at different orders to better learn node representations. The authors propose a variant of GCN, HWGCN, to consider convolution beyond 1-step neighbors, which is comparable to state-of-the-art methods.