Space–time density of trajectories: exploring spatio-temporal patterns in movement data

TLDR

Modern positioning technologies generate vast trajectory datasets, yet visualising them with conventional space–time cubes quickly becomes cluttered and unclear. The article introduces a 3D space–time density of trajectories to alleviate clutter in space–time cube visualisations. The authors generalise 2D kernel density to 3D polyline data, presenting an algorithm that computes a space–time density volume, which they test on simulated data and apply to real‑time AIS vessel trajectories. The resulting density volume reveals distinct spatio‑temporal patterns unique to trajectory data and suggests broader implications for spatial analysis.

Abstract

Modern positioning and identification technologies enable tracking of almost any type of moving object. A remarkable amount of new trajectory data is thus available for the analysis of various phenomena. In cartography, a typical way to visualise and explore such data is to use a space–time cube, where trajectories are shown as 3D polylines through space and time. With increasingly large movement datasets becoming available, this type of display quickly becomes cluttered and unclear. In this article, we introduce the concept of 3D space–time density of trajectories to solve the problem of cluttering in the space–time cube. The space–time density is a generalisation of standard 2D kernel density around 2D point data into 3D density around 3D polyline data (i.e. trajectories). We present the algorithm for space–time density, test it on simulated data, show some basic visualisations of the resulting density volume and observe particular types of spatio-temporal patterns in the density that are specific to trajectory data. We also present an application to real-time movement data, that is, vessel movement trajectories acquired using the Automatic Identification System (AIS) equipment on ships in the Gulf of Finland. Finally, we consider the wider ramifications to spatial analysis of using this novel type of spatio-temporal visualisation.