  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.
