Learning Latent Structure in Complex Networks

Latent structure in complex networks, e.g., in the form of community structure, can help understand network dynamics, identify heterogeneities in network properties, and predict ‘missing’ links. While most community detection algorithms are based on optimizing heuristic clustering objectives such as the Modularity, it has recently been shown that latent structure in complex networks is learnable by Bayesian generative link distribution models (Airoldi et al., 2008, Hofman and Wiggins, 2008). In this paper we propose a new generative model that allows representation of latent community structure as in the previous Bayesian approaches and in addition allows learning of node specific link properties similar to that in the modularity objective. We employ a new relaxation method for efficient inference in these generative models that allows us to learn the behavior of very large networks. We compare the link prediction performance of the learning based approaches and other widely used link prediction approaches in 14 networks ranging from medium size to large networks with more than a million nodes. While link prediction is typically well above chance for all networks, we find that the learning based mixed membership stochastic block model of Airoldi et al., performs well and often best in our experiments. The added complexity of the LD model improves link predictions for four of the 14 networks.