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.

翻译：移动实体集合可形成长时间共同移动的群组。追踪此类群组是野生动物生态学、城市交通或体育分析等多个领域的重要分析任务。相应地，近年来涌现出大量用于识别和追踪移动实体集合中有意义群组的算法。然而，不仅是一个或多个群组的存在这一事实值得发现；在许多应用领域中，群组的实际形态同样承载着重要信息。本文首次对移动群组的形态进行算法研究。我们采用核密度估计对群组内部密度进行建模，并展示了如何随时间高效维护该密度描述的近似值。此外，我们追踪持续性极大值点，这为群组时变形态提供了有意义的初步认知。通过结合多种近似技术，我们获得了一种能够高效近似追踪持续性极大值点的动力学数据结构。