{'fraction_non_alphanumeric': 0.029411764705882353, 'fraction_numerical': 0.0, 'mean_word_length': 5.16875, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A reduction of the dynamic time warping distance to the longest increasing subsequence length

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.