Link prediction based on higher-order structure extraction and autoencoder learning in directed networks

Abstract

Link prediction, which aims to estimate the likelihood of links based on the observed links and/or node attributes, is a common task in complex network analysis and graph data mining. Modeling and exploring high-order structure, also called network motif, are essential for understanding the fundamental structure that control and mediate the behavior of various complex systems. Most existing link prediction methods do not fully consider the high-order structure in the network. In addition, they mainly focus on undirected networks and therefore ignore the directionality of links. To this end, we propose a novel Autoencoder model based on high-order structure to solve the problems of existing link prediction methods. Specifically, we first provide an efficient motif adjacency matrix learning algorithm, which can be used to extract high-order structure in directed networks, and construct multiple motif adjacency matrices. Then, we extend the Graph Autoencoder (GAE) and Variational Autoencoder (VAE) frameworks to solve the link prediction problem in directed networks, which consists of three core modules. (i) First (Node Embedding): a novel encoder scheme is presented to learn the node embeddings from each motif adjacency matrix; (ii) Second (Information Fusion): a robust attention scheme is further introduced to aggregate information of node embeddings learned from multiple motif adjacency matrices to form the final semantically rich node embedding matrix; (iii) Third (Link Prediction): an efficient decoder scheme is finally proposed to reconstruct the target directed network in a multiscale way, by jointly utilizing node embeddings and PageRank centrality, the directions of links can be effectively inferred based on the classic gravitational heuristic formula. Extensive experiments were applied on various types of directed networks to validate the performance of our proposed approach through comparisons with the state-of-the-art link prediction technologies.