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.
Trajectory similarity is a fundamental task in analyzing mobility patterns, essential for applications such as route pattern extraction, mobility prediction, and anomaly detection. Traditional distance-based measures for computing similarity incur high computational cost, driving the adoption of lightweight learning-based approaches. Supervised methods rely on extensive labels derived from traditional distance measures and often reproduce these metrics, which limits generalization. While self-supervised learning addresses this issue through contrastive learning, it lacks a unified framework, making it difficult to compare deep learning (DL) models for consistent trajectory representation. Accordingly, this paper presents MoCo-AIS, a unified framework for learning vessel trajectory embeddings based on the Momentum Contrast (MoCo) paradigm, which formulates similarity learning through positive and negative trajectory pairs. Within this framework, we evaluate a diverse set of leading DL models on large-scale, real-world vessel-tracking AIS datasets that capture diverse navigation behaviors and operating conditions. Results demonstrate that our framework significantly improves similarity learning over existing baselines, while providing a benchmarking platform for evaluating trajectory representation models.