Geometric and Graph-based Approaches to Collective Motion

Summary

A trajectory is a time-stamped sequence of locations which represents the movement of entities in space. Trajectories are often created by sampling GPS locations and attaching a time-stamp, but they can also originate from RFID tags, video, or radar analysis. Huge data sets exist for entities as diverse as birds, deer, traveling humans, sports players, vehicles, and hurricanes.

During recent years analysis tools for trajectory data have been developed within the areas of GIScience and algorithms. Analysis objectives include clustering, performing similarity analysis, segmenting a trajectory into characteristic sub-trajectories, finding patterns like flocking, and several others. Since these computations are mostly spatial, algorithmic solutions have been developed in the areas of computational geometry and GIScience. Although trajectories store only the location of a single point of reference on a moving entity, this is acceptable for the common large-scale analysis tasks. However, for the study of more complex phenomena like interaction and collective motion, it is often insufficient and the basic trajectory representation must be extended.

Simultaneously, in the area of ecology the study of motion of animals has also become a topic of increasing interest. Many animal species move in groups, with or without a specific leader. The motivation for motion can be foraging, escape from predators, changing climate, or it can be unknown. The mode of movement can be determined by social interactions, energy efficiency, possibility of discovery of resources, and of course the natural environment. The more fascinating aspects of ecology include interaction between entities and collective motion. These are harder to grasp in a formal manner, needed for modelling and automated analysis.

The seminar brought together a group of enthusiastic researchers with a diverse background. To create a shared body of knowledge the seminar featured a number of survey talks that were planned early in the week. The survey talks were rather engaging: the audience learned for instance at what scale one should look at a painting of Van Gogh, how bats chase each other, what size of clumps mussels make and why, and how to interact with a computational geometer.

Probably the main research result was a momentum started up by interaction and awareness of an exciting direction of research where a lot can still be accomplished.

More specific research accomplishments included a methodology for evaluating whether fish or other animals have their movement mostly influenced by closest neighbors, and how to reconstruct movement just based on counts at different time steps.