Latent Space Modeling Approach for Temporal Networks

• Activity Number: 441
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Samrachana Adhikari* and Brian Junker
• Companies: Carnegie Mellon University and Carnegie Mellon University
• Keywords: Temporal networks ; Latent space network method ; Latent cluster model ; Bayesian analysis

Abstract

Interactions among entities in complex natural and socioeconomic systems can often be well represented by networks. These systems are governed by stochastic and dynamical processes, introducing noise and temporal dependencies in the networks. It is of scientific interest to gain insights into the organization and evolution of such systems by inferring the underlying structures of observed longitudinal networks.

We combine ideas from the state space and the latent variable network literatures, and introduce a Bayesian longitudinal latent space models. In this class of models, the networks are related to each other through the unobserved low dimensional latent space positions of the nodes. We explore models with two types of evolution in the latent structure. First, we model the evolution in the network as changes in individual nodal positions. Second, for networks with hierarchical structures we extend the model to allow for evolution through the changes in cluster means. We use MCMC algorithm for full posterior inference on the parameters. On simulated data and real world networks from education and adolescence health data we demonstrate a successful performance of our method.