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

2025-05-08

AI Summary

To address the discriminability challenge in time-series classification caused by temporal warping—particularly under single-shot learning where robustness and efficiency are difficult to reconcile—this paper introduces, for the first time, continuous optimal transport theory into time-series deformation modeling. We propose a Wasserstein-based heterogeneity measure that theoretically guarantees optimal solution recovery under single-sample conditions, achieving both warping robustness and low computational complexity. Compared to dynamic time warping (DTW), our method reduces time complexity by over an order of magnitude while maintaining—or even surpassing—the 1-nearest-neighbor (1NN) classification accuracy on both synthetic and real-world benchmarks. Our core contributions are threefold: (i) establishing a rigorous theoretical linkage between continuous optimal transport and temporal deformation; (ii) overcoming DTW’s inherent high-complexity bottleneck; and (iii) providing an efficient, interpretable paradigm for few-shot time-series classification.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Define a problem statement for time series classification under warping distortions
• Propose an efficient Optimal Transport-based dissimilarity measure for TSC
• Demonstrate the method's efficacy on simulated and real data

Innovation

• Continuous 1NN-DTW solves classification with one sample
• Optimal Transport measure reduces computational cost
• New approach tested on simulated and real data