Using Lower-Bound Representations for Trajectory Similarity Learning

2026-08-02

AI Summary

Existing learning-based approaches for trajectory similarity lack theoretical guarantees, exhibit weak generalization, and incur high training costs. This work proposes LB-TrajRep, the first unified trajectory lower-bound representation framework that dispenses with neural embeddings. Leveraging a point-pivot mechanism, LB-TrajRep generates single-vector representations that yield interpretable lower bounds for multiple classical distance measures—including Dynamic Time Warping (DTW), Hausdorff, and discrete Fréchet distance—and seamlessly integrates into standard vector retrieval pipelines. Two data-driven pivot selection strategies are introduced to optimize either bound tightness or hard-sample ranking quality. Experiments on real-world trajectory datasets demonstrate that LB-TrajRep significantly outperforms existing neural embedding methods, achieving 20%–60% gains in Top-k ranking accuracy for Hausdorff and discrete Fréchet distances and 15%–40% improvements for DTW.

Abstract

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.

Problem

• trajectory similarity learning
• distance measures
• lower-bound representation
• neural embeddings
• ranking accuracy

Innovation

• lower-bound representation
• trajectory similarity learning
• pivot selection
• vector-based retrieval
• distance approximation