(k, l)-Medians Clustering of Trajectories Using Continuous Dynamic Time Warping

Brankovic, Milutin; Buchin, Kevin; Klaren, Koen; Nusser, André; Popov, Aleksandr; Wong, Sampson

doi:10.1145/3397536.3422245

Cited by 21 publications

(15 citation statements)

References 22 publications

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“…Recent evidence has suggested that the travel pattern and actions of each individual animal may be influenced by the position and social status of another animal (Duvelle and Jeffery, 2018). Following this line of thought, we applied dynamic time warping, a method common in travel trajectory pattern comparisons (Brankovic et al, 2020), to compare similarities of trajectory patterns of a subject animal to that of a stranger or familiar mouse.…”

Section: Discussionmentioning

confidence: 99%

PyRodentTracks: flexible computer vision and RFID based system for multiple rodent tracking and behavioral assessment

Fong

Jury

et al. 2022

Preprint

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PyRodentTracks (PRT) is a scalable and customizable computer vision and RFID-based system for multiple rodent tracking and behavior assessment that can be set up within minutes in any user-defined arena at minimal cost. PRT is composed of the online Raspberry Pi-based video and RFID acquisition and the subsequent offline analysis tools. The system is capable of tracking up to 6 mice in experiments ranging from minutes to days. PRT maintained a minimum of 88% detections tracked with an overall accuracy >85% when compared to manual validation of videos containing 1-4 mice in a modified home-cage. As expected, chronic recording in home-cage revealed diurnal activity patterns. Moreover, it was observed that novel non-cagemate mice pairs exhibit more similarity in travel trajectory patterns over a 10-minute period in the openfield than cagemates. Therefore, shared features within travel trajectories between animals may be a measure of sociability that has not been previously reported. Moreover, PRT can interface with open-source packages such as Deeplabcut and Traja for pose estimation and travel trajectory analysis, respectively. In combination with Traja, PRT resolved motor deficits exhibited in stroke animals. Overall, we present an affordable, open-sourced, and customizable/scalable rodent-specific behavior recording and analysis system.

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Section: Discussionmentioning

confidence: 99%

PyRodentTracks: flexible computer vision and RFID based system for multiple rodent tracking and behavioral assessment

Fong

Jury

et al. 2022

Preprint

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“…There has been a lot of experimental work in clustering curves and point sets using the Fréchet, Hausdorff and other distances, e.g., see [9,30,21,6,26,3].…”

Section: Related Workmentioning

confidence: 99%

Coresets for $k$-median clustering under Fréchet and Hausdorff distances

Nath

2021

Preprint

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We give algorithms for computing coresets for (1 + ε)-approximate k-median clustering of polygonal curves (under the discrete and continuous Fréchet distance) and point sets (under the Hausdorff distance), when the cluster centers are restricted to be of low complexity. Ours is the first such result, where the size of the coreset is independent of the number of input curves/point sets to be clustered (although it still depends on the maximum complexity of each input object). Specifically, the size of the coreset is Θ k 3 lm δ d ε 2 log kl ε for any δ > 0, where d is the ambient dimension, m is the maximum number of points in an input curve/point set, and l is the maximum number of points allowed in a cluster center. We formally characterize a general condition on the restricted space of cluster centers -this helps us to generalize and apply the importance sampling framework, that was used by Langberg and Schulman for computing coresets for k-median clustering of d-dimensional points on normed spaces in R d , to the problem of clustering curves and point sets using the Fréchet and Hausdorff metrics. Roughly, the condition places an upper bound on the number of different combinations of metric balls that the restricted space of cluster centers can hit. We also derive lower bounds on the size of the coreset, given the restriction that the coreset must be a subset of the input objects.

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“…Their experiments show an improvement in map-matching when using CDTW instead of the Fréchet distance. In a recent paper, Brankovic et al [9] applied CDTW to clustering of bird migration data and handwritten character data. The authors used (k, )-center and medians clustering, where each of the k clusters has a (representative) center curve of complexity at most .…”

Section: Introductionmentioning

confidence: 99%

“…Low complexity center curves are used to avoid overfitting. Compared to DTW and the Fréchet distance, Brankovic et al [9] demonstrated that clustering under CDTW produced centers that were more visually similar to the expected center curve. Under DTW, the clustering quality deteriorated for small values of , whereas under the Fréchet distance, the clustering quality deteriorated in the presence of outliers.…”

Section: Introductionmentioning

confidence: 99%

Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time

Buchin¹,

Nusser²,

Wong³

2022

Preprint

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Dynamic Time Warping is arguably the most popular similarity measure for time series, where we define a time series to be a one-dimensional polygonal curve. The drawback of Dynamic Time Warping is that it is sensitive to the sampling rate of the time series. The Fréchet distance is an alternative that has gained popularity, however, its drawback is that it is sensitive to outliers.Continuous Dynamic Time Warping (CDTW) is a recently proposed alternative that does not exhibit the aforementioned drawbacks. CDTW combines the continuous nature of the Fréchet distance with the summation of Dynamic Time Warping, resulting in a similarity measure that is robust to sampling rate and to outliers. In a recent experimental work of Brankovic et al., it was demonstrated that clustering under CDTW avoids the unwanted artifacts that appear when clustering under Dynamic Time Warping and under the Fréchet distance. Despite its advantages, the major shortcoming of CDTW is that there is no exact algorithm for computing CDTW, in polynomial time or otherwise.In this work, we present the first exact algorithm for computing CDTW of one-dimensional curves. Our algorithm runs in time O(n 5 ) for a pair of one-dimensional curves, each with complexity at most n. In our algorithm, we propagate continuous functions in the dynamic program for CDTW, where the main difficulty lies in bounding the complexity of the functions. We believe that our result is an important first step towards CDTW becoming a practical similarity measure between curves.

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(k, l)-Medians Clustering of Trajectories Using Continuous Dynamic Time Warping

Cited by 21 publications

References 22 publications

PyRodentTracks: flexible computer vision and RFID based system for multiple rodent tracking and behavioral assessment

PyRodentTracks: flexible computer vision and RFID based system for multiple rodent tracking and behavioral assessment

Coresets for $k$-median clustering under Fréchet and Hausdorff distances

Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time

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