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On Map Construction, Map Comparison, and Trajectory Clustering

Geo-referenced trajectory data is collected in a wide range of applications, such as for a variety of locationbased services on street maps, hiking trail logging, and the study of social behavior in animals. There has been a recent surge of algorithms for aggregating trajectory data, in particular by constructing road maps, e.g., [1–3, 8–36]. Road map construction is a type of geometric reconstruction problem in which the task is to extract the underlying geometric graph structure described by a set of movement-constrained trajectories, or in other words reconstruct a geometric domain that has been sampled with continuous curves that are subject to noise. See Figures 1 and 2 for an example trajectory data set and different constructed road maps.