“…As a common data type, time series is a sequence of discrete data obtained from a target with a fixed frequency in a period. A fundamental task regarding the time series is to measure the similarity between two given ones, which is critical to downstream works in terms of classification [ 1 , 2 , 3 , 4 , 5 ], clustering [ 6 , 7 , 8 , 9 , 10 ] and pattern recognition [ 11 , 12 , 13 , 14 ]. The dynamic time warping (DTW) [ 15 ] algorithm and its variants [ 16 , 17 , 18 ] are competent in similarity evaluation [ 19 ].…”