A reduction of the dynamic time warping distance to the longest increasing subsequence length

Yoshifumi Sakai, Shunsuke Inenaga

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common subsequence (LCS) length and the edit distance. Although it may seem as if the DTW and the LCS(-like) measures are essentially different, we reveal that the DTW distance can be represented by the longest increasing subsequence (LIS) length of a sequence of integers, which is the LCS length between the integer sequence and itself sorted. For a given pair of time series of n integers between zero and c, we propose an integer sequence that represents any substring-substring DTW distance as its band-substring LIS length. The length of the produced integer sequence is O(c4n2) or O(c2n2) depending on the variant of the DTW distance used, both of which can be translated to O(n2) for constant cost functions. To demonstrate that techniques developed under the LCS(-like) measures are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.

本文言語英語
ホスト出版物のタイトル31st International Symposium on Algorithms and Computation, ISAAC 2020
編集者Yixin Cao, Siu-Wing Cheng, Minming Li
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ページ61-616
ページ数556
ISBN(電子版)9783959771733
DOI
出版ステータス出版済み - 12 2020
イベント31st International Symposium on Algorithms and Computation, ISAAC 2020 - Virtual, Hong Kong, 中国
継続期間: 12 14 202012 18 2020

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
181
ISSN(印刷版)1868-8969

会議

会議31st International Symposium on Algorithms and Computation, ISAAC 2020
Country中国
CityVirtual, Hong Kong
Period12/14/2012/18/20

All Science Journal Classification (ASJC) codes

  • Software

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