Tracking group co-membership on networks

Abstract

Tracking groups in network data is an emerging problem in network science. The network science community has not leveraged the tracking techniques used in data fusion, however. The purpose of this work is to introduce a novel domain to the tracking community, and novel techniques to network science. Group tracking is formulated here as a traditional, continuous-time Bayesian filter, which operates on time-evolving network data and outputs joint group membership probabilities over all nodes. Simple measurement and update models are proposed, which enable the derivation of an exact filter. This filter requires an exponentially large state space, however, so it is marginalized to a smaller space. The resulting system tracks second-order statistics (i.e., probabilities of pairs of nodes being in the same group) using equations involving third- and fourth-order statistics, which require closure assumptions. Several closures are investigated, and their merits and drawbacks are discussed.