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<p>Existing distance measures for time-series data are often neither effective nor efficient: most are not true metrics and typically incur quadratic computational cost with respect to time series length. In this paper, we propose a novel distance, called the Temporal Tree-Sliced Wasserstein (TTSW) distance, for time series data. TTSW quantifies differences between samples from the two time series using tree metrics. To integrate the temporal information within time series into the tree metrics, we present a tree-sampling procedure in which the structure of each sampled tree is determined through a clustering algorithm that partitions samples of time series based on differences in their temporal indices. Theoretical analyses show that TTSW is a true metric for time series and enjoys linear time complexity w.r.t. the time series length. We further study the applicability of TTSW in two tasks: time-series classification and clustering. Extensive experiments on widely used public datasets demonstrate the effectiveness and efficiency of TTSW compared to existing distance measures. Our code is available at <a href="https://github.com/TungDP/TTSW">https://github.com/TungDP/TTSW</a>.</p>

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Temporal Tree-Sliced Wasserstein distance for time-series data

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Tung Doan,
  • Duc Nguyen,
  • Hong Vuong

摘要

Existing distance measures for time-series data are often neither effective nor efficient: most are not true metrics and typically incur quadratic computational cost with respect to time series length. In this paper, we propose a novel distance, called the Temporal Tree-Sliced Wasserstein (TTSW) distance, for time series data. TTSW quantifies differences between samples from the two time series using tree metrics. To integrate the temporal information within time series into the tree metrics, we present a tree-sampling procedure in which the structure of each sampled tree is determined through a clustering algorithm that partitions samples of time series based on differences in their temporal indices. Theoretical analyses show that TTSW is a true metric for time series and enjoys linear time complexity w.r.t. the time series length. We further study the applicability of TTSW in two tasks: time-series classification and clustering. Extensive experiments on widely used public datasets demonstrate the effectiveness and efficiency of TTSW compared to existing distance measures. Our code is available at https://github.com/TungDP/TTSW.