Graph convolutional architectures via arbitrary order of information aggregation

Graph representation learning (GRL) has recently drawn a lot of attention due to its advantage in solving various machine learning tasks on graphs/networks, ranging from drug design to recommendation systems. One typical GRL approach is graph embedding, the purpose of which is to learn a map that encodes or represents network elements as points in a low-dimensional vector space so that downstream machine learning methods can be easily implemented. Initially, most graph embedding algorithms learn such a map independently from subsequent machine learning tasks. Therefore, they have limitations in solving supervised machine learning tasks on networks. Later, a great deal of graph convolutional networks (GCNs) have been proposed to learn node representations in an end-to-end manner based on different information aggregation mechanisms. By treating network structure as a computational layer in a GCN, the associated information of nodes with higher-order proximity can be aggregated by increasing the number of layers (i.e., depth) of the GCN. As a consequence, the computational overhead will increase and the representations will be projected towards a steady state. To solve this problem, in this paper, we propose a multi-channel graph convolutional network (MCGCN) that allows higher-order information aggregation by enriching the number of input channels. Based on the notion of Katz index, our model can further achieve an arbitrary order of information aggregation without increasing the computational overhead. Comprehensive experiments on several benchmark networks demonstrate the effectiveness of the proposed architecture by comparing it with the-state-of-art GRL methods in terms of node classification and computational efficiency.