Computing trajectory similarity is a fundamental operation in movement analytics, required in search, clustering, and classification of trajectories, for example. Yet the range of different but interrelated trajectory similarity measures can be bewildering for researchers and practitioners alike. This paper describes a systematic comparison and methodical exploration of trajectory similarity measures. Specifically, this paper compares five of the most important and commonly used similarity measures: dynamic time warping (DTW), edit distance (EDR), longest common subsequence (LCSS), discrete Fréchet distance (DFD), and Fréchet distance (FD). The paper begins with a thorough conceptual and theoretical comparison. This comparison highlights the similarities and differences between measures in connection with six different characteristics, including their handling of a relative versus absolute time and space, tolerance to outliers, and computational efficiency. The paper further reports on an empirical evaluation of similarity in trajectories with contrasting properties: data about constrained bus movements in a transportation network, and the unconstrained movements of wading birds in a coastal environment. A set of four experiments: a. creates a measurement baseline by comparing similarity measures to a single trajectory subjected to various transformations; b. explores the behavior of similarity measures on network-constrained bus trajectories, grouped based on spatial and on temporal similarity; c. assesses similarity with respect to known behavioral annotations (flight and foraging of oystercatchers); and d. compares bird and bus activity to examine whether they are distinguishable based solely on their movement patterns. The results show that in all instances both the absolute value and the ordering of similarity may be sensitive to the choice of measure. In general, all measures were more able to distinguish spatial differences in trajectories than temporal differences. The paper concludes with a high-level summary of advice and recommendations for selecting and using trajectory similarity measures in practice, with conclusions spanning our three complementary perspectives: conceptual, theoretical, and empirical.
In this article, a new morphing method is proposed for two linear features at different scales, based on their entire structures (MLBES in abbreviation). First, the bend structures of the linear features are identified by using a constrained Delaunay triangulation (CDT in abbreviation) model and represented by binary bend-structure trees. By matching the independent bends represented by the bend-structure trees, corresponding independent bends are obtained. These corresponding independent bends are further used to match their child bends based on hierarchical bend structures so that corresponding bends are obtained. On this basis, the two linear features are split into pairs of corresponding subpolylines by the start and end points of the corresponding bends. Second, structures of the corresponding subpolylines are identified by the Douglas-Peucker algorithm and represented by binary line generalization trees (BLGtrees in abbreviation). The corresponding subpolylines are split into smaller corresponding subpolylines by matching the nodes of the BLG-trees. Third, the corresponding points are identified by using the linear interpolation algorithm for every pair of corresponding subpolylines. Finally, straight-line trajectories are employed to generate a family of intermediate-scale linear features. By comparison with other methods, it is found that MLBES is accurate and efficient.
Graph is an intuitive and powerful tool to present relationships between entities. Efficiently visualizing graphs with node-link diagrams is a great challenge due to visual clutter induced by edge crossing and node-edge overlapping. Many edge bundling methods are proposed to disclose high-level edge patterns. Though previous methods can successfully reveal the coarse graph structure, the relation patterns at individual node level can be overlooked. In addition, many edge bundling algorithms are computationally complex to prevent them from scaling up for extremely large graphs. In this paper, we propose SideKnot, an efficient node-based bundling method to cluster and knot edges. SideKnot is light, runs faster than most existing algorithms, and can disclose the relation patterns of an individual node such as its standing in the graph and pattern of relations with its neighbors.
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