# Trainable Time Warping: Aligning Time-Series in the Continuous-Time Domain

arXiv: https://arxiv.org/abs/1903.09245 · HTML: https://mlsanity.com/paper/1903.09245/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Closed-Form Diffeomorphic Transformations for Time Series Alignment](https://mlsanity.com/paper/2206.08107/) (2022)
- [Deep Time Warping for Multiple Time Series Alignment](https://mlsanity.com/paper/2502.16324/) (2025)
- [Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces](https://mlsanity.com/paper/2506.01635/) (2025)

## Abstract (arXiv)

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 continuous-time domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on 85 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.