Density Approximation for Moving Groups (2212.03685v2)

Abstract: Sets of moving entities can form groups which travel together for significant amounts of time. Tracking such groups is an important analysis task in a variety of areas, such as wildlife ecology, urban transport, or sports analysis. Correspondingly, recent years have seen a multitude of algorithms to identify and track meaningful groups in sets of moving entities. However, not only the mere existence of one or more groups is an important fact to discover; in many application areas the actual shape of the group carries meaning as well. In this paper we initiate the algorithmic study of the shape of a moving group. We use kernel density estimation to model the density within a group and show how to efficiently maintain an approximation of this density description over time. Furthermore, we track persistent maxima which give a meaningful first idea of the time-varying shape of the group. By combining several approximation techniques, we obtain a kinetic data structure that can approximately track persistent maxima efficiently.