Active Sensing of Social Networks: Network Identification From Low-Rank Data

Learning the underlying structure of a social network and the influence of various agents is a fundamental problem for designing optimal actions, such as targeted advertisement. In many studies the structure of the network is assumed to be known based on the existence of an interaction or because the agents have professed a friendship. However, it is more reasonable to assume that the underlying opinion dynamics are shaped by a weighted directed graph that is latent. Therefore, it is crucial to estimate the strength of the agents' influence on each other to single out which interactions have little effect on the dynamics versus those that truly matter. The goal of this chapter is to explore how polarized opinions can be used to identify the weighted directed network graph that captures the agents' mutual influence, based on either passive or active observations. Opinion dynamics models provide the mathematical underpinning for the low-rank structure exhibited in rating and opinion polling data, especially when the data are drawn from a social network, supporting the observation that real-world opinions are often polarized. We begin with an overview of social dynamics models. Then, we concentrate on the well-known DeGroot dynamics and demonstrate that sparsity and low-rank conditions provide superior performance over other conventional techniques and provide examples of applications. We also show how inserting active agents into the network can significantly enhance our ability to sense the network. We conclude with a number of interesting research problems and extensions.