ABSTRACT

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.

摘要

计算轨迹相似度是运动分析中的一项基本操作，例如，在轨迹的搜索、聚类和分类中需要。然而，不同但相互关联的轨迹相似性度量的范围可能让研究人员和从业人员都感到困惑。本文描述了轨迹相似性度量的系统比较和有条不紊的探索。具体来说，本文比较了五个最重要和最常用的相似性度量：动态时间扭曲（DTW）、编辑距离（EDR）、最长公共子序列（LCSS）、离散弗雷谢距离（DFD）和弗雷谢距离（FD）。本文首先对概念和理论进行了彻底的比较。这种比较突出了与六个不同特征相关的措施之间的异同，包括他们对相对与绝对时间和空间的处理、对异常值的容忍度以及计算效率。该论文进一步报告了对具有对比特性的轨迹相似性的实证评估：关于交通网络中受约束的公共汽车运动的数据，以及沿海环境中涉水鸟类的不受约束的运动。一组四个实验： a．通过将相似性度量与经受各种变换的单个轨迹进行比较来创建度量基线；湾 探索基于空间和时间相似性分组的网络受限总线轨迹上的相似性度量行为；C。评估与已知行为注释（牡蛎捕食者的飞行和觅食）的相似性；和 d。比较鸟类和公共汽车的活动，以检查它们是否可以仅根据它们的运动模式进行区分。结果表明，在所有情况下，绝对值和相似度的排序都可能对度量的选择很敏感。一般而言，所有措施都比时间差异更能区分轨迹中的空间差异。本文最后对在实践中选择和使用轨迹相似性度量的建议和建议进行了高级总结，结论涵盖了我们三个互补的观点：概念、理论和经验。所有措施都比时间差异更能区分轨迹的空间差异。本文最后对在实践中选择和使用轨迹相似性度量的建议和建议进行了高级总结，结论涵盖了我们三个互补的观点：概念、理论和经验。所有措施都比时间差异更能区分轨迹的空间差异。本文最后对在实践中选择和使用轨迹相似性度量的建议和建议进行了高级总结，结论涵盖了我们三个互补的观点：概念、理论和经验。