# Trajectory Similarity Measurement: An Efficiency Perspective

arXiv: https://arxiv.org/abs/2311.00960 · HTML: https://mlsanity.com/paper/2311.00960/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2023.

## Built on by (most cited first, 16 of 16)

- [Trajectory Data Management and Mining: A Survey from Deep Learning to the LLM Era](https://mlsanity.com/paper/2403.14151/) (2024)
- [UniTraj: Learning a Universal Trajectory Foundation Model from Billion-Scale Worldwide Traces](https://mlsanity.com/paper/2411.03859/) (2024)
- [FlexiReg: Flexible Urban Region Representation Learning](https://mlsanity.com/paper/2503.09128/) (2025)
- [Self-Supervised Representation Learning for Geospatial Objects: A Survey](https://mlsanity.com/paper/2408.12133/) (2024)
- [SIMformer: Single-Layer Vanilla Transformer Can Learn Free-Space Trajectory Similarity](https://mlsanity.com/paper/2410.14629/) (2024)
- [Revisiting CNNs for Trajectory Similarity Learning](https://mlsanity.com/paper/2405.19761/) (2024)
- [A Survey of Distance-Based Vessel Trajectory Clustering: Data Pre-processing, Methodologies, Applications, and Experimental Evaluation](https://mlsanity.com/paper/2407.11084/) (2024)
- [Contrast & Compress: Learning Lightweight Embeddings for Short Trajectories](https://mlsanity.com/paper/2506.02571/) (2025)
- [TSMini: A Simple Yet Highly Effective Trajectory Similarity Learning Model](https://mlsanity.com/paper/2502.00285/) (2025)
- [Computational Analysis of Character Development in Holocaust Testimonies](https://mlsanity.com/paper/2412.17063/) (2024)
- [Learning Generalized and Flexible Trajectory Models from Omni-Semantic Supervision](https://mlsanity.com/paper/2505.17437/) (2025)
- [UrbanVerse: Learning Urban Region Representation Across Cities and Tasks](https://mlsanity.com/paper/2602.15750/) (2026)
- [FedTDP: A Privacy-Preserving and Unified Framework for Trajectory Data Preparation via Federated Learning](https://mlsanity.com/paper/2505.05155/) (2025)
- [GeoPTH: A Lightweight Approach to Category-Based Trajectory Retrieval via Geometric Prototype Trajectory Hashing](https://mlsanity.com/paper/2511.16258/) (2025)
- [MoCo-AIS: A Contrastive Learning Framework for Similarity Computation of Vessel Trajectories](https://mlsanity.com/paper/2606.17978/) (2026)
- [Using Lower-Bound Representations for Trajectory Similarity Learning](https://mlsanity.com/paper/2608.01039/) (2026)

## Abstract (arXiv)

Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic measures, e.g., Hausdorff or ERP, that operate directly on the trajectories. In contrast, recent studies exploit deep learning to map trajectories to d-dimensional vectors, called embeddings. Then, some distance measure, e.g., Manhattan or Euclidean, is applied to the embeddings to quantify trajectory similarity. The resulting similarities are inaccurate: they only approximate the similarities obtained using the heuristic measures. As distance computation on embeddings is efficient, focus has been on achieving embeddings yielding high accuracy. Adopting an efficiency perspective, we analyze the time complexities of both the heuristic and the learning-based approaches, finding that the time complexities of the former approaches are not necessarily higher. Through extensive experiments on open datasets, we find that, on both CPUs and GPUs, only a few learning-based approaches can deliver the promised higher efficiency, when the embeddings can be pre-computed, while heuristic approaches are more efficient for one-off computations. Among the learning-based approaches, the self-attention-based ones are the fastest to learn embeddings that also yield the highest accuracy for similarity queries. These results have implications for the use of trajectory similarity approaches given different application requirements.