Group diagrams for representing trajectories

Buchin, Maike; Kilgus, Bernhard; Kölzsch, Andrea

doi:10.1080/13658816.2019.1684498

Cited by 10 publications

(6 citation statements)

References 20 publications

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“…In a series of papers, these ideas were also applied to the problem of reconstructing road maps from GPS data [7,8]. In a similar vain, Buchin, Kilgus and Kölzsch [10] studied the trajectories of migrating animals and defined so-called group diagrams which are meant to represent the underlying migration patterns in the form of a graph. In their algorithm, to build the group diagram, they repeatedly find the largest cluster and remove it from the data, inspired by the classical greedy set cover algorithm.…”

Section: Related Workmentioning

confidence: 99%

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Faster Approximate Covering of Subcurves under the Fréchet Distance

Frederik¹,

Jacobus²,

Driemel³

2022

Preprint

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Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of a set cover problem for a given polygonal curve: find the smallest number k of representative curves such that any point on the input curve is contained in a subcurve that has Fréchet distance at most a given ∆ to a representative curve. We focus on the case where the representative curves are line segments and approach this NP-hard problem with classical techniques from the area of geometric set cover: we use a variant of the multiplicative weights update method which was first suggested by Brönniman and Goodrich for set cover instances with small VC-dimension. We obtain a bicriteria-approximation algorithm that computes a set of O(k log(k)) line segments that cover a given polygonal curve of n vertices under Fréchet distance at most O(∆). We show that the algorithm runs in O(k 2 n + kn 3 ) time in expectation and uses O(kn + n 3 ) space. For two dimensional input curves that are c-packed, we bound the expected running time by O(k 2 c 2 n) and the space by O(kn + c 2 n). In R d the dependency on n instead is quadratic. In addition, we present a variant of the algorithm that uses implicit weight updates on the candidate set and thereby achieves near-linear running time in n without any assumptions on the input curve, while keeping the same approximation bounds. This comes at the expense of a small (polylogarithmic) dependency on the relative arclength.

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Section: Related Workmentioning

confidence: 99%

“…One line of research uses the well-established Fréchet distance to define similarity between subcurves, for example the works of Agarwal et al [1], Buchin et al [10] and Akitaya et al [2].…”

Section: Introductionmentioning

confidence: 99%

Faster Approximate Covering of Subcurves under the Fréchet Distance

Frederik¹,

Jacobus²,

Driemel³

2022

Preprint

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“…Trajectories, as the basic unit of spatial analysis, free geospatial researchers from the static-location confinement for insights into the temporally connected locations to inform patterns of life and human dynamics [55]. Trajectory mining has gained popularity in geospatial research with a rich suite of methods and applications [29] and continues to enjoy fast development of new methods in recent years, especially on semantic trajectory modeling that relates trajectories to travel modes, purposes, or social implications [31] and on group movements [8] and spatial community structures [16].…”

Section: Compute Events For Discovering An Event's Dynamic Structurementioning

confidence: 99%

“…Popular studies are limited to identifying event clusters, their patterns over space and time, and their correlations to other objects or events. Exceptions are trajectories with time-stamped locations over the course of a movement, such as taxi-and-limousine trip record data in New York City, USA 8 plus intermediate stops (e.g., hurricane tracks 9 and GeoLife GPS trajectories 10 ).…”

Section: Introductionmentioning

confidence: 99%

Why are events important and how to compute them in geospatial research?

Yuan¹

2020

JOSIS

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Geospatial research has long centered around objects. While attention to events is growing rapidly, events remain objectified in spatial databases. This paper aims to highlight the importance of events in scientific inquiries and overview general event-based approaches to data modeling and computing. As machine learning algorithms and big data become popular in geospatial research, many studies appear to be the products of convenience with readily adaptable data and codes rather than curiosity. By asking why events are important and how to compute events in geospatial research, the author intends to provoke thinking into the rationale and conceptual basis of event-based modeling and to emphasize the epistemological role of events in geospatial information science. Events are essential to understanding the world and communicating the understanding, events provide points of entry for knowledge inquiries and the inquiry processes, and events mediate objects and scaffold causality. We compute events to improve understanding, but event computing and computability depend on event representation. The paper briefly reviews event-based data models in spatial databases and methods to compute events for site understanding and prediction, for spatial impact assessment, and for discovering events' dynamic structures. Concluding remarks summarize key arguments and comment on opportunities to extend event computability.

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“…Specifically, this special section was proposed as part of a pre-conference workshop on Analysis of Movement Data (AMD 2018) at the GIScience 2018 meeting, 28 August 2018, Melbourne, Australia. The focus of this special section is on three aspects of CMA: (1) representation and modeling of movement (Buchin et al 2019, Graser et al 2020; (2) urban mobility analytics (Qiang andXu 2019, Li et al 2020) and (3) movement analytics using social media data (Ma et al 2020, Xin andMacEachren 2020). With the papers presented in the special section, we highlight recent advancements in CMA with the development of methods and techniques for big movement data analytics and utilization of trajectories constructed using user-generated crowdsourced contents such as geo-tagged social media posts.…”

Section: Introductionmentioning

confidence: 99%