Multi-layer graph analytics for social networks

Brandon Oselio, Alex Kulesza, Alfred O. Hero
2013 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
Modern social networks frequently encompass multiple distinct types of connectivity information; for instance, explicitly acknowledged friend relationships might complement behavioral measures that link users according to their actions or interests. One way to represent these networks is as multi-layer graphs, where each layer contains a unique set of edges over the same underlying vertices (users). Edges in different layers typically have related but distinct semantics; depending on the
more » ... tion, multiple layers might be used to reduce noise through averaging, perform multifaceted analyses, or a combination of the two. However, it is not obvious how to extend standard graph analysis techniques to the multi-layer setting in a flexible way. In this paper we develop latent variable models and methods for mining multi-layer networks for connectivity patterns based on noisy data. Multi-layer networks arise naturally when we have more than one source of connectivity information for a group of users. In a social networking context, we often have knowledge of direct communication links, i.e., relational information. However, we might also derive behavioral relationships based on user actions or interests. The question that this paper attempts to address is how to deal with these multiple layers of a social network when attempting to perform tasks like inference, clustering, and anomaly detection. We propose a generative hierarchical latent-variable model for multi-layer networks, and show how to perform inference on its parameters. Using techniques from Bayesian Model Averaging [1], we conditionally decouple the layers of the network using a latent selection variable; this makes it possible to write the posterior probability of the latent variables given the multi-layer network. The resulting mixture can be viewed as a scalarization of a multi-objective optimization problem [2], [3], [4] . When the posterior probability functions are convex, the scalarization of the multiobjective problem is both optimal and consistent with the Bayesian context [2], [5] . We then step back from the Bayesian setting and discuss how multi-objective optimization can be used to perform MAP estimation of the desired latent variables. Using the concept of Pareto optimality [4], we can define an entire front of solutions; this allows a user to define a preference over optimization functions and tune the algorithm accordingly. The result is a level of supervised optimization and inference that still utilizes the structure of multi-layer networks. We perform experiments on a simulated example, showing that our method yields improved clustering performance in noisy conditions. We discuss how our framework can be combined with existing models, and describe the details of The authors are with the
doi:10.1109/camsap.2013.6714063 dblp:conf/camsap/OselioKH13 fatcat:murl4cojqndafdpzehav3u7wcm