eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
6:1
6:16
10.4230/LIPIcs.ISAAC.2020.6
article
A Reduction of the Dynamic Time Warping Distance to the Longest Increasing Subsequence Length
Sakai, Yoshifumi
1
Inenaga, Shunsuke
2
3
Graduate School of Agricultural Science, Tohoku University, Sendai, Japan
Department of Informatics, Kyushu University, Fukuoka, Japan
PRESTO, Japan Science and Technology Agency, Kawaguchi, Japan
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(c⁴ n²) or O(c² n²) 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.6/LIPIcs.ISAAC.2020.6.pdf
algorithms
dynamic time warping distance
longest increasing subsequence
semi-local sequence comparison