How to compare movement? A review of physical movement similarity measures in geographic information science and beyond

In geographic information science, a plethora of different approaches and methods is used to assess the similarity of movement. Some of these approaches term two moving objects similar if they share akin paths. Others require objects to move at similar speed and yet others consider movement similar if it occurs at the same time. We believe that a structured and comprehensive classification of movement comparison measures is missing. We argue that such a classification not only depicts the status quo of qualitative and quantitative movement analysis, but also allows for identifying those aspects of movement for which similarity measures are scarce or entirely missing. In this review paper we, first, decompose movement into its spatial, temporal, and spatiotemporal movement parameters. A movement parameter is a physical quantity of movement, such as speed, spatial path, or temporal duration. For each of these parameters we then review qualitative and quantitative methods of how to compare movement. Thus, we provide a systematic and comprehensive classification of different movement similarity measures used in geographic information science. This classification is a valuable first step toward a GIS toolbox comprising all relevant movement comparison methods.