Maximum error-bounded Piecewise Linear Representation for online stream approximation

Handle URI:
http://hdl.handle.net/10754/563490
Title:
Maximum error-bounded Piecewise Linear Representation for online stream approximation
Authors:
Xie, Qing ( 0000-0003-4530-588X ) ; Pang, Chaoyi; Zhou, Xiaofang; Zhang, Xiangliang ( 0000-0002-3574-5665 ) ; Deng, Ke
Abstract:
Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer Science Program; Machine Intelligence & kNowledge Engineering Lab
Publisher:
Springer Nature
Journal:
The VLDB Journal
Issue Date:
4-Apr-2014
DOI:
10.1007/s00778-014-0355-0
Type:
Article
ISSN:
10668888
Sponsors:
This research is partially supported by Natural Science Foundation of China (Grant No. 61232006) and the Australian Research Council (Grant No. DP140103171 and DP130103051).
Appears in Collections:
Articles; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorXie, Qingen
dc.contributor.authorPang, Chaoyien
dc.contributor.authorZhou, Xiaofangen
dc.contributor.authorZhang, Xiangliangen
dc.contributor.authorDeng, Keen
dc.date.accessioned2015-08-03T11:52:45Zen
dc.date.available2015-08-03T11:52:45Zen
dc.date.issued2014-04-04en
dc.identifier.issn10668888en
dc.identifier.doi10.1007/s00778-014-0355-0en
dc.identifier.urihttp://hdl.handle.net/10754/563490en
dc.description.abstractGiven a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.en
dc.description.sponsorshipThis research is partially supported by Natural Science Foundation of China (Grant No. 61232006) and the Australian Research Council (Grant No. DP140103171 and DP130103051).en
dc.publisherSpringer Natureen
dc.subjectError bounden
dc.subjectPiecewise Linear Representationen
dc.subjectStream approximationen
dc.titleMaximum error-bounded Piecewise Linear Representation for online stream approximationen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentComputer Science Programen
dc.contributor.departmentMachine Intelligence & kNowledge Engineering Laben
dc.identifier.journalThe VLDB Journalen
dc.contributor.institutionAEHRC, CSIROBrisbane, Australiaen
dc.contributor.institutionZhejiang University (NIT)Ningbo, Chinaen
dc.contributor.institutionHebei Academy of SciencesHebei, Chinaen
dc.contributor.institutionSchool of Information Technology and Electrical Engineering, The University of QueenslandBrisbane, Australiaen
dc.contributor.institutionSchool of Computer Science and Technology, Soochow UniversitySuzhou, Chinaen
dc.contributor.institutionHuawei Noah’s Ark Research LabHong Kong, Chinaen
kaust.authorXie, Qingen
kaust.authorZhang, Xiangliangen
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