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An algorithm for continuous piecewise linear bounding of discrete time series data

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Abstract

An algorithm for enclosing a given set of time series data inside a continuous piecewise linear band of varying height subject to certain constraints is presented. The band is defined by two piecewise linear curves that lie above and below the data respectively. Segments of these curves are constrained to start and end at one of the data points, and those whose slope does not lie between its neighbors’ slopes are required to be at least as wide as a user-specified value. The algorithm yields a band which accurately preserves the general trends of the data, while enclosing the inherent measurement noise. This band is typically obtained in \(O(n\log K)\) time, where \(n\) is the number of data points and \(K\) is the number of linear segments. The algorithm is described and its capabilities are tested on four data sets. Comparisons are made with alternative algorithms.

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Authors and Affiliations

  1. University of Guelph, Guelph, ON, Canada

    Andrew Skelton & Allan R. Willms

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  1. Andrew Skelton
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  2. Allan R. Willms
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Correspondence to Andrew Skelton.

Additional information

Communicated by Rosemary Renaut.

This work was supported by an Ontario Graduate Scholarship and a Natural Sciences and Engineering Council of Canada Discovery Grant.

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Skelton, A., Willms, A.R. An algorithm for continuous piecewise linear bounding of discrete time series data. Bit Numer Math 54, 1155–1169 (2014). https://doi.org/10.1007/s10543-014-0492-2

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  • DOI: https://doi.org/10.1007/s10543-014-0492-2

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