An Efficient Transport-Based Dissimilarity Measure for Time Series Classification under Warping Distortions

TL;DR

This paper introduces a new transport-based dissimilarity measure for time series classification that effectively handles warping distortions and reduces computational costs compared to traditional methods like DTW.

Contribution

The paper proposes a novel optimal transport-based dissimilarity measure for time series classification, offering theoretical insights and practical advantages over classic DTW.

Findings

The transport-based measure effectively handles warping distortions.

It achieves comparable or better accuracy than DTW in experiments.

The method significantly reduces computational complexity.

Abstract

Time Series Classification (TSC) is an important problem with numerous applications in science and technology. Dissimilarity-based approaches, such as Dynamic Time Warping (DTW), are classical methods for distinguishing time series when time deformations are confounding information. In this paper, starting from a deformation-based model for signal classes we define a problem statement for time series classification problem. We show that, under theoretically ideal conditions, a continuous version of classic 1NN-DTW method can solve the stated problem, even when only one training sample is available. In addition, we propose an alternative dissimilarity measure based on Optimal Transport and show that it can also solve the aforementioned problem statement at a significantly reduced computational cost. Finally, we demonstrate the application of the newly proposed approach in simulated and real time series classification data, showing the efficacy of the method.