  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.
