Network modelling and variational Bayesian inference for structure analysis of signed networks

Currently, structure analysis of signed networks with positive and negative links has received wide attention and is becoming a research focus in the area of network science. In recent years, many community detection methods for signed networks have been proposed to analyze the structure of signed networks. However, current methods can only efficiently analyze the signed networks with the single community structure and unable to analyze the signed networks with the coexisting structure of communities and peripheral nodes, bipartite, or other structures. To address this problem, in this study, we present a mathematically principled method for the structure analysis of signed networks with positive and negative links, in which a probabilistic model firstly is proposed to model the signed networks with the single community or the coexisting structure, and a variational Bayesian approach is deduced to learn the approximate distribution of model parameters. For determining the optimal model, we also deduce a model selection criterion based on the evidence theory. In addition, to efficiently analyze the large signed networks, we propose a fast learning version of our algorithm with the time complexity O(k²E) where k is the number of groups and E is the number of links. In our experiments, the proposed method is validated in the synthetic and real-world signed networks, and is compared with the state-of-the-art methods. The experimental results demonstrate that the proposed method can more efficiently and accurately analyze to the structure of signed networks than the state-of-the-art methods.