Spatiotemporal Interactive Modeling of Event-Based Dynamic Networks

Event-based dynamic networks exist in a wide range of areas, including traffic, biological, and social applications. Such a network consists of interaction event sequences over different locations, where each event may trigger or influence a series of subsequent events under certain intrinsic spatial structure because of their geographical and semantic proximities. Such influence patterns and triggering motivations reflect the nature and semantics of human/object behaviors in the network. Thus, modeling event-based dynamic networks properly is critically important. This article proposes a spatiotemporal interactive Hawkes process (SIHP) that describes how a series of events occurs and models the rate of interaction events between any pair of nodes on the network explicitly with the information from related historical events as well as geographical and semantic neighboring nodes. The proposed SIHP can not only learn the patterns of influence from historical interaction events on later ones, but can also understand the network dynamics by fully considering spatial structure knowledge. Specifically, we incorporate prior knowledge of spatial structure as a graph and design graph regularization in the SIHP, where model parameters are estimated by designing an alternating direction method of multiplier (ADMM) framework. Numerical experiments and a real case study on New York yellow taxi data validate the effectiveness of the proposed method.