Group diagrams for representing trajectories

Given the trajectories of one or several moving groups, we propose a new framework, the group diagram (GD) for representing these. Specifically, we seek a minimal GD as a concise representation of the groups maintaining the spatio-temporal structure of the groups' movement. A GD is specified by three input values, namely a distance threshold, a similarity measure and a minimality criterion. For several variants of the GD, we give a comprehensive analysis of their computational complexity and present efficient approximation algorithms for their computation. Furthermore, we experimentally evaluate our algorithms on GPS data of migrating geese. Applying the proposed methods on these data sets reveals how the GD concisely represents the movement of the groups. This representation can be used for further analysis and for the formulation of new hypotheses for further ecological research, such as differences in movement patterns of groups on different surfaces or the shift of migration routes over several years. We use different similarity measures to summarize the migration routes of (i) a goose family for one migration period and to summarize (ii) the migration routes of one individual for several migration periods or (iii) the migration routes of several independent individuals for one migration period.