Density Approximation for Moving Groups

TL;DR

This paper introduces a method to approximate and track the evolving shape of moving groups using kernel density estimation and persistent maxima, providing insights into group dynamics over time.

Contribution

It presents a novel approach to model and track the shape of moving groups by combining density approximation and persistent maxima within a kinetic data structure.

Findings

Efficiently maintains density approximations over time.

Tracks persistent maxima to understand group shape dynamics.

Provides a framework for analyzing group shape evolution.

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.