Applying classical detection and tracking theory to networks

Three related network problems are considered which illustrate the applicability of signal processing techniques to network science. The first is to determine whether a subnetwork is anomalous: this is framed as a simple binary detection problem that leads to complex likelihood ratio computations. The second is the community detection problem: many algorithms for this exist, but applying Bayesian decision theory leads to a new class of solutions. The third is the generalization of community detection to a tracking problem. Introducing an appropriate stochastic evolution model leads to a Kalman-filter-like solution.