# OTW: Optimal Transport Warping for Time Series

arXiv: https://arxiv.org/abs/2306.00620 · HTML: https://mlsanity.com/paper/2306.00620/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 8 of 8)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [D3TW: Discriminative Differentiable Dynamic Time Warping for Weakly Supervised Action Alignment and Segmentation](https://mlsanity.com/paper/1901.02598/) (2019)
- [End-to-End Adversarial Text-to-Speech](https://mlsanity.com/paper/2006.03575/) (2020)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Differentiable Divergences Between Time Series](https://mlsanity.com/paper/2010.08354/) (2020)
- [Spatio-Temporal Alignments: Optimal transport through space and time](https://mlsanity.com/paper/1910.03860/) (2019)
- [DeepNAG: Deep Non-Adversarial Gesture Generation](https://mlsanity.com/paper/2011.09149/) (2020)

## Built on by (most cited first, 2 of 2)

- [A Survey on Algorithmic Developments in Optimal Transport Problem with Applications](https://mlsanity.com/paper/2501.06247/) (2025)
- [Geometry-Conditioned Fixed-Scaffold Encoders for Time-Warp Robust Sequence Retrieval](https://mlsanity.com/paper/2609.36809/) (2026)

## Abstract (arXiv)

Dynamic Time Warping (DTW) has become the pragmatic choice for measuring distance between time series. However, it suffers from unavoidable quadratic time complexity when the optimal alignment matrix needs to be computed exactly. This hinders its use in deep learning architectures, where layers involving DTW computations cause severe bottlenecks. To alleviate these issues, we introduce a new metric for time series data based on the Optimal Transport (OT) framework, called Optimal Transport Warping (OTW). OTW enjoys linear time/space complexity, is differentiable and can be parallelized. OTW enjoys a moderate sensitivity to time and shape distortions, making it ideal for time series. We show the efficacy and efficiency of OTW on 1-Nearest Neighbor Classification and Hierarchical Clustering, as well as in the case of using OTW instead of DTW in Deep Learning architectures.