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An improved algorithm for segmenting online time series with error bound guarantee

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Abstract

In many real application, the volume of time series data increases seriously. How to store and process data becomes more interesting and challenge things. Effective representations can make storage less, processing more easily. In this paper, we contribute to construct a new piecewise linear approximation algorithm for segmenting online time series with error bound guarantee. To beat our targets, we combine a disconnected segment strategy into Feasible Space Window method, and to test our algorithm, we compare with algorithms that adopts the above strategies on both real and synthetic data sets. The time complexity of our algorithm is O(n) and the number of segments is smaller than FSW algorithm on all tested data sets.

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Abbreviations

δ:

A given error bound on each data point

P :

A time series

F :

A set of linear line

p k :

The k-th data point in time series

\( \widetilde{{p_{k} }} \) :

The k-th intersection by represent line

\( \underline{{p_{i} }} \) :

Data point with deleted tolerant error

\( \overline{{p_{i} }} \) :

Data point with added tolerant error

p start :

The starting point

p next :

The next coming data point

\( p_{{t_{e} }} \) :

The data point at which the FSW becomes empty

\( p_{{t_{e} }}^{'} \) :

The joint point at t e

u :

An upper boundary line

l :

A lower boundary line

n s :

The number of segments

\( \underline{{p_{{t_{e} }} }} \) :

The intersection point at t e by l

\( \overline{{p_{{t_{e} }} }} \) :

The intersection point at t e by u

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Acknowledgments

This work was supported by the Science and Technology Key Project of Hebei Academy of Sciences under Grant No. 2014055306 and the cooperation project between Chinese Academy of Sciences and Hebei Academy of Sciences.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Hebei Academy of Sciences, Shijiazhuang, 050081, China

    Huan-yu Zhao

  2. Department of Information Engineering, Shijiazhuang University of Economics, Shijiazhuang, 050031, China

    Guang-xia Li

  3. NIT, Zhejiang University, Ningbo, 315100, China

    Hao-lan Zhang

  4. Guangzhou Higher Education Mega Centre, South China Normal University, Guangzhou, 500006, China

    Yun Xue

Authors
  1. Huan-yu Zhao
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  2. Guang-xia Li
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  3. Hao-lan Zhang
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  4. Yun Xue
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Correspondence to Hao-lan Zhang.

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Zhao, Hy., Li, Gx., Zhang, Hl. et al. An improved algorithm for segmenting online time series with error bound guarantee. Int. J. Mach. Learn. & Cyber. 7, 365–374 (2016). https://doi.org/10.1007/s13042-014-0310-9

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  • DOI: https://doi.org/10.1007/s13042-014-0310-9

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