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

## TL;DR

This paper introduces Trainable Time Warping (TTW), a novel algorithm for fast, high-quality alignment of multiple time-series in the continuous-time domain, outperforming existing methods on various datasets.

## Contribution

The paper presents TTW, a new linear-complexity, continuous-time alignment method using sinc convolution and gradient optimization, addressing limitations of previous algorithms.

## Key findings

- TTW outperforms GTW on 67.1% of datasets for averaging.
- TTW outperforms GTW on 61.2% of datasets for classification.
- TTW has linear complexity in both number and length of time-series.

## Abstract

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.