# Aligning Time Series on Incomparable Spaces

arXiv: https://arxiv.org/abs/2006.12648 · HTML: https://mlsanity.com/paper/2006.12648/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

## Built on by (most cited first, 16 of 16)

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- [Leveraging Optimal Transport for Enhanced Offline Reinforcement Learning in Surgical Robotic Environments](https://mlsanity.com/paper/2310.08841/) (2023)
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- [Variable-Frequency Imitation Learning for Variable-Speed Motion](https://mlsanity.com/paper/2411.12310/) (2024)
- [On Combining Expert Demonstrations in Imitation Learning via Optimal Transport](https://mlsanity.com/paper/2307.10810/) (2023)
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- [Measuring dissimilarity with diffeomorphism invariance](https://mlsanity.com/paper/2202.05614/) (2022)
- [An Evaluation of Low Overhead Time Series Preprocessing Techniques for Downstream Machine Learning](https://mlsanity.com/paper/2209.05300/) (2022)
- [Financial time series augmentation using transformer based GAN architecture](https://mlsanity.com/paper/2602.17865/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Relational Synthesis: Structure-Mediated Concatenative Synthesis for Foley and Retrieval-Augmented Audio Generation](https://mlsanity.com/paper/2610.05768/) (2026)

## Abstract (arXiv)

Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.