License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.22
URN: urn:nbn:de:0030-drops-160307
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16030/
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Buchin, Kevin ; Nusser, André ; Wong, Sampson

Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time

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LIPIcs-SoCG-2022-22.pdf (1 MB)

Abstract

Dynamic Time Warping is arguably the most popular similarity measure for time series, where we define a time series to be a one-dimensional polygonal curve. The drawback of Dynamic Time Warping is that it is sensitive to the sampling rate of the time series. The Fréchet distance is an alternative that has gained popularity, however, its drawback is that it is sensitive to outliers.
Continuous Dynamic Time Warping (CDTW) is a recently proposed alternative that does not exhibit the aforementioned drawbacks. CDTW combines the continuous nature of the Fréchet distance with the summation of Dynamic Time Warping, resulting in a similarity measure that is robust to sampling rate and to outliers. In a recent experimental work of Brankovic et al., it was demonstrated that clustering under CDTW avoids the unwanted artifacts that appear when clustering under Dynamic Time Warping and under the Fréchet distance. Despite its advantages, the major shortcoming of CDTW is that there is no exact algorithm for computing CDTW, in polynomial time or otherwise.
In this work, we present the first exact algorithm for computing CDTW of one-dimensional curves. Our algorithm runs in time ?(n⁵) for a pair of one-dimensional curves, each with complexity at most n. In our algorithm, we propagate continuous functions in the dynamic program for CDTW, where the main difficulty lies in bounding the complexity of the functions. We believe that our result is an important first step towards CDTW becoming a practical similarity measure between curves.

BibTeX - Entry

@InProceedings{buchin_et_al:LIPIcs.SoCG.2022.22,
  author =	{Buchin, Kevin and Nusser, Andr\'{e} and Wong, Sampson},
  title =	{{Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16030},
  URN =		{urn:nbn:de:0030-drops-160307},
  doi =		{10.4230/LIPIcs.SoCG.2022.22},
  annote =	{Keywords: Computational Geometry, Curve Similarity, Fr\'{e}chet distance, Dynamic Time Warping, Continuous Dynamic Time Warping}
}

Keywords: Computational Geometry, Curve Similarity, Fréchet distance, Dynamic Time Warping, Continuous Dynamic Time Warping
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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