# Time Series Alignment with Global Invariances

arXiv: https://arxiv.org/abs/2002.03848 · HTML: https://mlsanity.com/paper/2002.03848/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [Cross-Domain Imitation Learning via Optimal Transport](https://mlsanity.com/paper/2110.03684/) (2021)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averaging](https://mlsanity.com/paper/2502.06591/) (2025)
- [Averaging Spatio-temporal Signals using Optimal Transport and Soft Alignments](https://mlsanity.com/paper/2203.05813/) (2022)
- [Personalized Convolutional Dictionary Learning of Physiological Time Series](https://mlsanity.com/paper/2503.07687/) (2025)
- [TimePoint: Accelerated Time Series Alignment via Self-Supervised Keypoint and Descriptor Learning](https://mlsanity.com/paper/2505.23475/) (2025)
- [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)
- [A Differentiable Alignment Framework for Sequence-to-Sequence Modeling via Optimal Transport](https://mlsanity.com/paper/2502.01588/) (2025)

## Abstract (arXiv)

Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as soon as the temporal dynamics and the representation of the time series, em i.e. the nature of the observed quantities, differ from one another. In this work, we propose a novel distance accounting both feature space and temporal variabilities by learning a latent global transformation of the feature space together with a temporal alignment, cast as a joint optimization problem. The versatility of our framework allows for several variants depending on the invariance class at stake. Among other contributions, we define a differentiable loss for time series and present two algorithms for the computation of time series barycenters under this new geometry. We illustrate the interest of our approach on both simulated and real world data and show the robustness of our approach compared to state-of-the-art methods.