Algorithms for Summarizing, Representing, and Analyzing Trajectories of Moving Objects

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The analysis of spatio-temporal trajectory data for sets of moving objects is quickly becoming an important area of research for which efficient geometric algorithms are necessary. The decreased cost and size of GPS-enabled devices and motion-tracking sensors has led to a tremendous increase in the number and use of devices for recording motion, quickly creating extensive demand for processing and analysis of sets of trajectories by a variety of applications: migratory patterns of animals; fleets of commercial vehicles; routes of cyclists, hikers, and runners on trails; commercial interests in analyzing the motion of shoppers in malls; motion-capture data used in the creation of video games or computer animation; government analysis of the movement of cell-phone users upon receiving an emergency message; sports analytics of player tracking data; etc. The development of efficient algorithms for supporting these tasks is essential, and would represent a significant contribution that would directly benefit a wide range of applications that involve motion. Most existing geometric optimization algorithms operate on static input, e.g., on a given set of points, line segments, polyhedra, etc. The same holds for most existing notions of centrality, data depth, location estimators, and clustering objective functions. Motivated by the multitude of present-day applications involving motion, and the ease, prevalence, and variety of methods for recording motion, the proposed research seeks to develop efficient algorithms for simplifying, summarizing, representing, and analyzing moving input. Specifically, the algorithms operate on sets of spatio-temporal trajectories representing the positions of objects moving through space over time. The proposed research program's objectives include: 1.Identifying good location estimators and summary statistics for spatio-temporal trajectory data, including defining new measures of centrality and data depth that effectively summarize and represent the input set of motions, along with efficient algorithms for computing these, and 2.Defining appropriate objective functions for partitioning sets of moving objects into clusters based on the similarities of their spatio-temporal trajectories, along with efficient algorithms for computation. The broader goal is to develop new ideas and new techniques to efficiently summarize, represent, and analyze motion and the trajectories of groups of moving objects. The proposed research will involve training approximately 15 HQP who will develop expertise relevant to the large variety of Canadian industries whose business involves trajectory data and motion.