Time Series Alignment with Global Invariances

TL;DR

This paper introduces a novel, flexible distance measure for multivariate time series that jointly learns global feature transformations and temporal alignments, improving robustness and versatility in various applications.

Contribution

It proposes a new joint optimization framework for time series alignment that accounts for feature and temporal variabilities, including differentiable loss and barycenter algorithms.

Findings

Demonstrates robustness on simulated and real data

Outperforms state-of-the-art methods in alignment tasks

Provides versatile variants for different invariance classes

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, {\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.