Time-integrated Optimal Transport: A Robust Minimax Framework

TL;DR

This paper introduces the Time-integrated Optimal Transport (TiOT) framework, a parameter-free, unified metric for comparing time series that combines temporal alignment and feature similarity, with efficient computation and improved accuracy.

Contribution

The paper presents TiOT, a novel, parameter-free optimal transport-based framework for time series comparison that integrates temporal and feature information into a unified metric.

Findings

Achieves improved accuracy on synthetic and real-world datasets

Maintains computational efficiency comparable to existing methods

Provides a well-defined metric with properties similar to Wasserstein distance

Abstract

Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based approaches often depend on manually selected balancing parameters and can be computationally intensive. In this work, we introduce the Time-integrated Optimal Transport (TiOT) framework, which integrates temporal and feature components into a unified objective and yields a well-defined metric on the space of probability measures. This metric preserves fundamental properties of the Wasserstein distance, while avoiding the need for parameter tuning. To address the corresponding computational challenges, we introduce an entropic regularized approximation of TiOT, which can be efficiently solved using a block coordinate descent algorithm. Extensive experiments on both synthetic and real-world time series datasets demonstrate that our approach achieves improved accuracy and stability while maintaining comparable efficiency.