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In the past two decades, Piecewise Linear Approximation under maximum error (max-error) bound (PLA \(_\infty \) ) has been intensively studied for effective qualified representation and analysis of time series data. It divides a time series into fragments and then represents each fragment with a straight line to approximate the data points of that time slot. In this paper, to elevate the representation quality in the optimal PLA \(_\infty \) results, we present a linear-time algorithm \({\text{ FindMin }}\) to construct the unique line representative of minimized maximum error (min-max error) for each fragment. Through extended experimental tests, we demonstrate that the proposed algorithm is very efficient in execution and achieves better performances than the state-of-the-art solutions.

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Representation with Minimized Max-Error in Optimal Piecewise Linear Approximation of Time Series Data

  • 会议论文

  • 发表日期：

    2025年

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  • Huanyu Zhao,
  • Tongliang Li,
  • Shiting Wen,
  • Zhenyu Shu,
  • Ke Deng,
  • Jian Yang,
  • Chaoyi Pang

摘要

In the past two decades, Piecewise Linear Approximation under maximum error (max-error) bound (PLA \(_\infty \) ) has been intensively studied for effective qualified representation and analysis of time series data. It divides a time series into fragments and then represents each fragment with a straight line to approximate the data points of that time slot. In this paper, to elevate the representation quality in the optimal PLA \(_\infty \) results, we present a linear-time algorithm \({\text{ FindMin }}\) to construct the unique line representative of minimized maximum error (min-max error) for each fragment. Through extended experimental tests, we demonstrate that the proposed algorithm is very efficient in execution and achieves better performances than the state-of-the-art solutions.