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    Maximum error-bounded Piecewise Linear Representation for online stream approximation

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    Type
    Article
    Authors
    Xie, Qing cc
    Pang, Chaoyi
    Zhou, Xiaofang
    Zhang, Xiangliang cc
    Deng, Ke
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Machine Intelligence & kNowledge Engineering Lab
    Date
    2014-04-04
    Online Publication Date
    2014-04-04
    Print Publication Date
    2014-12
    Permanent link to this record
    http://hdl.handle.net/10754/563490
    
    Metadata
    Show full item record
    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.
    Citation
    Xie, Q., Pang, C., Zhou, X., Zhang, X., & Deng, K. (2014). Maximum error-bounded Piecewise Linear Representation for online stream approximation. The VLDB Journal, 23(6), 915–937. doi:10.1007/s00778-014-0355-0
    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).
    Publisher
    Springer Nature
    Journal
    The VLDB Journal
    DOI
    10.1007/s00778-014-0355-0
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00778-014-0355-0
    Scopus Count
    Collections
    Articles; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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