Median trajectories using well-visited regions and shortest paths

Kreveld, Marc van; Wiratma, Lionov

doi:10.1145/2093973.2094006

Cited by 10 publications

(4 citation statements)

References 13 publications

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“…It cannot, however, deal with other loops, and it has a high running time of roughly O(M 2 N 2 ). van Kreveld and Wiratma (2011) proposed the majority median, which is built from input edges that are close to many other input edges. This algorithm also has a high asymptotic running time of O(M 3 N 3 logM N ).…”

Section: Central Trajectorymentioning

confidence: 99%

“…For one, the temporal and spatial dimensions are handled differently. Some approaches (Buchin et al 2010, van Kreveld and Wiratma 2011, Lee et al 2007, Petitjean et al 2011 ignore the temporal dimension, and work only in the spatial domain. Other approaches (Etienne et al 2010, Har-Peled and Raichel 2014) take both dimensions into account.…”

Section: Central Trajectorymentioning

confidence: 99%

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Trajectory Box Plot: a new pattern to summarize movements

Emmanuel

Devogèle

Buchin

et al. 2015

International Journal of Geographical Information Science

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International audienceNowadays, an abundance of sensors are used to collect very large datasets of moving objects. The movement of these objects can be analysed by identifying common routes. For this, a cluster of trajectories must be defined and the pattern of each cluster discovered. In this article, we introduce a new pattern, called the Trajectory Box Plot (TBP), to summarize a set of trajectories following the same route. The TBP is an extension of the well-known descriptive statistics Box Plot concept. Each TBP is described by a median trajectory, a 3D box and a 3D fence. The median trajectory depicts the typical movement of mobile objects. The box and the fences (whiskers) describe the spatial and temporal spreading around the central tendency. TBPs are useful to summarize and analyse trajectory streams, understand their spatio-temporal density and detect outliers. In this article, visual analysis highlights how the TBP pattern effectively describes how the density of trajectory clusters change over time

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Section: Central Trajectorymentioning

confidence: 99%

Section: Central Trajectorymentioning

confidence: 99%

Trajectory Box Plot: a new pattern to summarize movements

Emmanuel

Devogèle

Buchin

et al. 2015

International Journal of Geographical Information Science

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“…An analysis of tracks of moving points is called "trajectory analysis", namely trajectory smoothing [13] (for reducing errors in positioning), trajectory clustering [14][15][16][17] (for retrieving similar trajectories from a database), prediction of movement [18,19], representative path extraction [15,17,[20][21][22] and an algorithm for labeling positioning data [23].…”

Section: Trajectory Analysis and Density Estimatorsmentioning

confidence: 99%

Moving Point Density Estimation Algorithm Based on a Generated Bayesian Prior

Asahara¹,

Hayashi²,

Kai³

2015

IJGI

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To improve decision making, real-time population density must be known. However, calculating the point density of a huge dataset in real time is impractical in terms of processing time. Accordingly, a fast algorithm for estimating the distribution of the density of moving points is proposed. The algorithm, which is based on variational Bayesian estimation, takes a parametric approach to speed up the estimation process. Although the parametric approach has a drawback, that is the processes to be carried out on the server are very slow, the proposed algorithm overcomes the drawback by using the result of an estimation of an adjacent past density distribution.

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“…Computing a representative curve is a well studied problem [11,25,21,15,24,3,12,13]. For similar (close) monotone trajectories with the same start and end vertices, Buchin, et al [11] presented algorithms for computing the median trajectory and the homotopic median trajectory.…”

Section: Introductionmentioning

confidence: 99%

Approximating The p-Mean Curve of Large Data-Sets

Aghamolaei,

Ghodsi

2020

Preprint

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Given p, k and a set of polygonal curves P1, . . . , PL, the pmean curve M of P1, . . . , PL is the curve with at most k vertices that minimizes the Lp norm of the vector of Fréchet distances between each Pi and M . Also, the p-mean curve is the cluster representative (center) of Lp-based clusterings such as k-center, k-medians, and k-means. For p → ∞, this problem is known to be NP-hard, with lower bound 2.25 − on its approximation factor for any > 0. By relaxing the number of vertices to O(k), we were able to get constant factor approximation algorithms for p-mean curve with p = O(1) and p → ∞, for curves with few changes in their directions.

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Median trajectories using well-visited regions and shortest paths

Cited by 10 publications

References 13 publications

Trajectory Box Plot: a new pattern to summarize movements

Trajectory Box Plot: a new pattern to summarize movements

Moving Point Density Estimation Algorithm Based on a Generated Bayesian Prior

Approximating The p-Mean Curve of Large Data-Sets

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