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   Chen, Zhengyu ; Gu, Jie ( February 2021 , IEEE Journal of Solid-State Circuits)

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3. Trainable Time Warping: Aligning Time-series in the Continuous-time Domain

   https://doi.org/10.1109/icassp.2019.8682322  

   Khorram, Soheil ; McInnis, Melvin G ; Mower Provost, Emily ( May 2019 , International Conference on Acoustics, Speech, and Signal Processing (ICASSP))

   DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series length. The exception is generalized time warping (GTW), which has linear computational cost. Yet, it can only identify simple time warping functions. There is a need for a new fast, high-quality multisequence alignment algorithm. We introduce trainable time warping (TTW), whose complexity is linear in both the number and the length of time-series. TTW performs alignment in the continuoustime domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on S5 UCR datasets in time-series averaging and classification. TTW outperforms GTW on 67.1% of the datasets for the averaging tasks, and 61.2% of the datasets for the classification tasks. 

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