用下界表示法提升轨迹相似性学习,无需神经网络也能更准更快。
Using Lower-Bound Representations for Trajectory Similarity Learning
- 构建轨迹的单向量下界表示,可适配多种经典距离度量。
- 在真实数据集上,对齐距和弗雷歇距离排名准确率提升20%~60%。
- 适合需要可解释性和高效检索的轨迹分析场景。
轨迹相似性学习是复杂距离度量下高效轨迹检索的基础。现有基于学习的方法通常依赖于逼近轨迹距离或排序的嵌入表示,但往往缺乏对原始距离的保证,跨距离度量表现不稳定,且训练成本高。本文从下界表示的角度重新审视轨迹相似性学习,提出无需深度神经网络嵌入的统一框架LB-TrajRep。该框架通过一组下界分量构造单向量表示,为动态时间规整(DTW)、豪斯多夫距离和离散弗雷歇距离等经典轨迹距离提供可接纳且可解释的下界。在此框架内,我们设计点-枢轴分量,自然支持度量与非度量距离,并兼容标准向量检索流程。为进一步提升排序质量,提出两种数据驱动的枢轴选择策略:分别优化下界紧致性与优先处理困难近邻对。在多个真实轨迹数据集上的大量实验表明,所提下界表示在不同距离度量下均持续优于最先进神经嵌入方法,对豪斯多夫距离和弗雷歇距离的top-$k$排名准确率提升达20%–60%,对DTW提升15%–40%。
原文摘要 · Abstract (English)
Trajectory similarity learning is fundamental to efficient trajectory retrieval under complex distance measures. Existing learning-based methods typically rely on embeddings trained to approximate trajectory distances or rankings, but they often lack guarantees with respect to the original distances, exhibit unstable performance across distance measures, and incur substantial training costs. We revisit trajectory similarity learning from a lower-bound representation perspective and propose LB-TrajRep, a unified lower-bound representation framework independent of deep neural embeddings. This framework constructs single-vector representations from a set of lower-bound components, enabling admissible and interpretable lower bounds for multiple classical trajectory distances, including Dynamic Time Warping (DTW), Hausdorff distance, and Discrete Fréchet Distance (DFD). Within this framework, we instantiate point-pivot components, which naturally support both metric and non-metric distances and remain compatible with standard vector-based retrieval pipelines. To improve ranking quality, we develop two data-driven pivot selection strategies that explicitly optimize lower-bound tightness and prioritize hard near-neighbor trajectory pairs, respectively. Extensive experiments on real-world trajectory datasets show that the proposed lower-bound representations are able to consistently outperform state-of-the-art neural trajectory embeddings across diverse distance measures, improving top-$k$ ranking accuracy by up to 20\%--60\% on the Hausdorff distance and DFD and by 15\%--40\% on DTW.
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