Time Series Alignment with Global Invariances

Titouan Vayer, Romain Tavenard, Laetitia Chapel, Rémi Flamary, Nicolas Courty, Yann Soullard

Abstract: 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, 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.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission:

We would first like to thank reviewer LTHj for their feedback, and, as for reviewers 1VCa and JXeQ, for their insightful suggestions that we believe helped us improve the paper.
We have implemented the modifications they have asked in an updated version of our paper, in which changes from the previous iteration in the text appear in blue. Modifications are detailed in the answer we provide below.

Code: https://github.com/rtavenar/dtw_gi

Assigned Action Editor: ~Nicolas_THOME2

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 380