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

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

Abstract: 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.