Network representation learning method embedding linear and nonlinear network structures

With the rapid development of neural networks, much attention has been focused on network embedding for complex network data, which aims to learn low-dimensional embedding of nodes in the network and how to effectively apply learned network representations to various graph-based analytical tasks. Two typical models exist namely the shallow random walk network representation method and deep learning models such as graph convolution networks (GCNs). The former one can be used to capture the linear structure of the network using depth-first search (DFS) and width-first search (BFS), whereas Hierarchical GCN (HGCN) is an unsupervised graph embedding that can be used to describe the global nonlinear structure of the network via aggregating node information. However, the two existing kinds of models cannot simultaneously capture the nonlinear and linear structure information of nodes. Thus, the nodal characteristics of nonlinear and linear structures are explored in this paper, and an unsupervised representation method based on HGCN that joins learning of shallow and deep models is proposed. Experiments on node classification and dimension reduction visualization are carried out on citation, language, and traffic networks. The results show that, compared with the existing shallow network representation model and deep network model, the proposed model achieves better performances in terms of micro-F1, macro-F1 and accuracy scores.