Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time
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Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time. / Buchin, Kevin; Nusser, André; Wong, Sampson.
38th International Symposium on Computational Geometry, SoCG 2022. ed. / Xavier Goaoc; Michael Kerber. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. 22 (Leibniz International Proceedings in Informatics, LIPIcs, Vol. 224).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Computing Continuous Dynamic Time Warping of Time Series in Polynomial Time
AU - Buchin, Kevin
AU - Nusser, André
AU - Wong, Sampson
N1 - Publisher Copyright: © Kevin Buchin, Andr Nusser, and Sampson Wong; licensed under Creative Commons License CC-BY 4.0
PY - 2022
Y1 - 2022
N2 - 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 O(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.
AB - 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 O(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.
KW - Computational Geometry
KW - Continuous Dynamic Time Warping
KW - Curve Similarity
KW - Dynamic Time Warping
KW - Fréchet distance
U2 - 10.4230/LIPIcs.SoCG.2022.22
DO - 10.4230/LIPIcs.SoCG.2022.22
M3 - Article in proceedings
AN - SCOPUS:85134330651
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 38th International Symposium on Computational Geometry, SoCG 2022
A2 - Goaoc, Xavier
A2 - Kerber, Michael
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 38th International Symposium on Computational Geometry, SoCG 2022
Y2 - 7 June 2022 through 10 June 2022
ER -
ID: 342674199