A reduction of the dynamic time warping distance to the longest increasing subsequence length
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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 measurements including the longest common subsequence (LCS) length and the edit distance. Although it may seem as if the DTW and LCS(-like) measurements 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. To demonstrate that techniques developed under LCS(-like) measurements 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.
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