Convolution Based Graph Representation Learning from the Perspective of High Order Node Similarities

Nowadays, graph representation learning methods, in particular graph neural network methods, have attracted great attention and performed well in many downstream tasks. However, most graph neural network methods have a single perspective since they start from the edges (or adjacency matrix) of graphs, ignoring the mesoscopic structure (high-order local structure). In this paper, we introduce HS-GCN (High-order Node Similarity Graph Convolutional Network), which can mine the potential structural features of graphs from different perspectives by combining multiple high-order node similarity methods. We analyze HS-GCN theoretically and show that it is a generalization of the convolution-based graph neural network methods from different normalization perspectives. A series of experiments have shown that by combining high-order node similarities, our method can capture and utilize the high-order structural information of the graph more effectively, resulting in better results.