**Multi-layer graph analysis for dynamic social networks**

Multi-layer graph analysis for dynamic social networks Multi-layer networks arise naturally when there exists more than one source of connectivity information for a group of users. For Multi-layer graph analysis for dynamic social networks instance, in a social networking context there is often knowledge of direct communication links, i.e., relational information. Examples of Multi-layer graph analysis for dynamic social networks relational information include the frequency with which users communicate over social media, or whether a user has sent or Multi-layer graph analysis for dynamic social networks recei

ved emails from another user in a given time period. However, it is also possible to derive behavioral relationships based on user actions Multi-layer graph analysis for dynamic social networks or interests. These behavioral relationships are inferred from information that does not directly connect users, such as individual preferences or usage statistics. In this paper we show how to deal with multiple layers of a social network when performing tasks like inference, clustering, and anomaly detection. We Multi-layer graph analysis for dynamic social networks 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 the layers of the network are conditionally Multi-layer graph analysis for dynamic social networks decoupled 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 When the posterior probability functions are convex, the scalarization is Multi-layer graph a

**Multi-layer graph analysis for dynamic social network**

nalysis for dynamic social networks both optimal and consistent with the Bayesian principle of model-averaged inference 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 an entire front of solutions is Multi-layer graph analysis for dynamic social networks defined; 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 utilizes the structure of multi-layer networks without scalarization. Experiments on a simulated example show that our method yields improved clustering performance

in noisy conditions. The developed framework is then Multi-layer graph analysis for dynamic social networks combined with the dynamic stochastic block model (DSBM) which captures a variety of complex temporal network phenomena. Finally, the multilayer DSBM is applied to a real-world data set drawn from the ENRON email corpus. This example illustrates how we can combine two layers of a network to explore complex connections through both time and layer mixing parameters.