# Autowarp: Learning a Warping Distance from Unlabeled Time Series Using Sequence Autoencoders

arXiv: https://arxiv.org/abs/1810.10107 · HTML: https://mlsanity.com/paper/1810.10107/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2018.

## Built on by (most cited first, 14 of 14)

- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Uncertainty-DTW for Time Series and Sequences](https://mlsanity.com/paper/2211.00005/) (2022)
- [T-Rep: Representation Learning for Time Series using Time-Embeddings](https://mlsanity.com/paper/2310.04486/) (2023)
- [Towards Similarity-Aware Time-Series Classification](https://mlsanity.com/paper/2201.01413/) (2022)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [TILDE-Q: A Transformation Invariant Loss Function for Time-Series Forecasting](https://mlsanity.com/paper/2210.15050/) (2022)
- [Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Paths](https://mlsanity.com/paper/2303.10778/) (2023)
- [Anomaly Detection in Event-triggered Traffic Time Series via Similarity Learning](https://mlsanity.com/paper/2506.16855/) (2025)
- [Towards Measuring and Modeling Geometric Structures in Time Series Forecasting via Image Modality](https://mlsanity.com/paper/2507.23253/) (2025)
- [SrvfNet: A Generative Network for Unsupervised Multiple Diffeomorphic Shape Alignment](https://mlsanity.com/paper/2104.13449/) (2021)
- [DTWSSE: Data Augmentation with a Siamese Encoder for Time Series](https://mlsanity.com/paper/2108.09885/) (2021)
- [Visual Time Series Forecasting: An Image-driven Approach](https://mlsanity.com/paper/2107.01273/) (2021)
- [Task-aware Similarity Learning for Event-triggered Time Series](https://mlsanity.com/paper/2207.08159/) (2022)
- [Self-Supervised State Space Model for Real-Time Traffic Accident Prediction Using eKAN Networks](https://mlsanity.com/paper/2409.05933/) (2024)

## Abstract (arXiv)

Measuring similarities between unlabeled time series trajectories is an important problem in domains as diverse as medicine, astronomy, finance, and computer vision. It is often unclear what is the appropriate metric to use because of the complex nature of noise in the trajectories (e.g. different sampling rates or outliers). Domain experts typically hand-craft or manually select a specific metric, such as dynamic time warping (DTW), to apply on their data. In this paper, we propose Autowarp, an end-to-end algorithm that optimizes and learns a good metric given unlabeled trajectories. We define a flexible and differentiable family of warping metrics, which encompasses common metrics such as DTW, Euclidean, and edit distance. Autowarp then leverages the representation power of sequence autoencoders to optimize for a member of this warping distance family. The output is a metric which is easy to interpret and can be robustly learned from relatively few trajectories. In systematic experiments across different domains, we show that Autowarp often outperforms hand-crafted trajectory similarity metrics.