Rotation invariant distance measures for trajectories

Vlachos, Michail; Gunopulos, Dimitrios; Das, Gautam

doi:10.1145/1014052.1014144

Cited by 76 publications

(60 citation statements)

References 17 publications

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“…Dynamic time warping (DTW) [14] has been used for trajectory similarity. Furthermore, trajectory similarity measures have been developed based on longest common subsequences (LCSS) [22], dynamic time warping (DTW) [23], and edit distance [8]. These measures all differ in nature to the average distance at corresponding times.…”

Section: Subtrajectory Similaritymentioning

confidence: 99%

Finding long and similar parts of trajectories

Buchin

Kreveld

et al. 2009

Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

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A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines with time stamps. For the case when a minimum duration of the subtrajectories is specified and the subtrajectories must start at corresponding times, we give a linear-time algorithm. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value. In the case that the subtrajectories may start at non-corresponding times, it appears difficult to give exact algorithms, even if the duration of the subtrajectories is fixed. For this case, we give (1 + ε)-approximation algorithms, for both fixed duration and when only a minimum duration is specified.

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Section: Subtrajectory Similaritymentioning

confidence: 99%

Finding long and similar parts of trajectories

Buchin

Kreveld

et al. 2009

Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

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“…Lee et al also developed approaches for trajectory clustering [11] based on sub-trajectories. Vlachos et al present a DTW-based distance measure that is invariant to rotation in [21].…”

Section: Related Workmentioning

confidence: 99%

“…Respective tasks include trajectory clustering, classification, and k-nearest neighbor search. Several approaches and distance measures have been proposed, tailored to multi-dimensional object trajectories, e.g., [3,20,21]. Common to all the existing approaches is that distances measures (or functions) are explicitly given as part of the framework.…”

Section: Introductionmentioning

confidence: 99%

Constraint-Based Learning of Distance Functions for Object Trajectories

Wei

Gertz

2009

Lecture Notes in Computer Science

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Abstract.With the drastic increase of object trajectory data, the analysis and exploration of trajectories has become a major research focus with many applications. In particular, several approaches have been proposed in the context of similarity-based trajectory retrieval. While these approaches try to be comprehensive by considering the different properties of object trajectories at different degrees, the distance functions are always pre-defined and therefore do not support different views on what users consider (dis)similar trajectories in a particular domain.In this paper, we introduce a novel approach to learning distance functions in support of similarity-based retrieval of multi-dimensional object trajectories. Our approach is more generic than existing approaches in that distance functions are determined based on constraints, which specify what object trajectory pairs the user considers similar or dissimilar. Thus, using a single approach, different distance functions can be determined for different users views. We present two learning techniques, transformed Euclidean distance and transformed Dynamic Time Warping. Both techniques determine a linear transformation of the attributes of multi-dimensional trajectories, based on the constraints specified by the user. We demonstrate the flexibility and efficiency of our approach with applications to clustering and classification on real and synthetic object trajectory datasets from different application domains.

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“…• When only the second element in the triple is the MBR of a segment (line [23][24], the first node is expanded by calling expandElement, with elem1 and elem2 exchanged.…”

Section: Nearest Neighbor Joinmentioning

confidence: 99%

“…[13] considers similarity search for trajectories using spatio-temporal indices and proposes a novel distance measure, however the work does not address the similarity join of trajectories. We note that the constructing MBRs over time series data for lower bounding has been explored for other similarity measures along with the idea of early abandoning [17], [23], [27]. In this respect, we applied our wDF distance and combine similarity joins and spatio-temporal indices in the native space of moving object trajectories [7], [18], [20] …”

Section: Related Workmentioning

confidence: 99%