A comparative analysis of trajectory similarity measures

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.

Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time

“…Computing similarities is also a fundamental building block for other analyses, such as clustering, classification, or simplification. There are numerous similarity measures considered in literature [4,18,22,25,36,39], many of which are application dependent.…”

Across atoms to crossing continents: application of similarity measures to biological location data

“…[1][2][3] An ongoing challenge is to quantify and compare sequential spatiotemporal processes, which can involve confounding environmental and individual-based factors, as well as be affected by the frequency, accuracy, and precision of measurement. 4 Various measures of data similarity have been applied to classify and compare individual movement trajectories in both anthropogenic and ecological applications, [5][6][7] and submolecular-scale movements of proteins. 8,9 Biological data sets inevitably contain noise, for example, through limits in measurement precision and accuracy, but also through actual movement not relevant to the questions of interest.…”

“…Recent studies have highlighted the broad usability of similarity measures to distinguish among known contrasting synthetically simulated and measured trajectories. 5,6…”

“…9 On the macroscopic level , the migratory orientation and movement of birds are also influenced by the Earth’s magnetic field, 16,17 and can also be assessed using similarity measures. 5,6 Differences between their individual flight trajectories can additionally be important in assessing ecological hazards, conservation concerns and anthropogenic impacts. 21,22 For example, the migratory songbird Northern Wheatear ( Oenanthe oenan-the ) undertakes twice-yearly cross-continental journeys between Alaska and Africa.…”

“…Recent studies have highlighted the broad usability of similarity measures to distinguish among known contrasting synthetically simulated and measured trajectories. 5,6 To demonstrate how similarity measures can be used in life sciences, we have applied the similarity measures listed in Table 1 to two distinct but related examples. The measures were applied to biological data related to magnetic field sensing in migratory birds.…”