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GeoPTH: A Lightweight Approach to Category-Based Trajectory Retrieval via Geometric Prototype Trajectory Hashing

Yang Xu, Zuliang Yang, Kai Ming Ting

TL;DR

Trajectory category retrieval has been hampered by expensive traditional metrics and heavy training costs in learning-based methods. GeoPTH provides a lightweight, non-learning solution that maps trajectories to binary codes by vector-quantizing against geometric prototypes and using the Hausdorff distance $d_H$, yielding codes of length $L=\omega M$. By concatenating $M$ $\omega$-bit sub-hashes, GeoPTH achieves competitive accuracy with traditional metrics and learning-based methods while delivering orders-of-magnitude efficiency gains. The approach is robust to noise via prototype ensembles and benefits from the metric properties of $d_H$, enabling scalable, fast retrieval on large trajectory collections. Future work could explore smarter prototype selection and integration of temporal or semantic cues to capture richer category information.

Abstract

Trajectory similarity retrieval is an important part of spatiotemporal data mining, however, existing methods have the following limitations: traditional metrics are computationally expensive, while learning-based methods suffer from substantial training costs and potential instability. This paper addresses these problems by proposing Geometric Prototype Trajectory Hashing (GeoPTH), a novel, lightweight, and non-learning framework for efficient category-based trajectory retrieval. GeoPTH constructs data-dependent hash functions by using representative trajectory prototypes, i.e., small point sets preserving geometric characteristics, as anchors. The hashing process is efficient, which involves mapping a new trajectory to its closest prototype via a robust, Hausdorff metric. Extensive experiments show that GeoPTH's retrieval accuracy is highly competitive with both traditional metrics and state-of-the-art learning methods, and it significantly outperforms binary codes generated through simple binarization of the learned embeddings. Critically, GeoPTH consistently outperforms all competitors in terms of efficiency. Our work demonstrates that a lightweight, prototype-centric approach offers a practical and powerful alternative, achieving an exceptional retrieval performance and computational efficiency.

GeoPTH: A Lightweight Approach to Category-Based Trajectory Retrieval via Geometric Prototype Trajectory Hashing

TL;DR

Trajectory category retrieval has been hampered by expensive traditional metrics and heavy training costs in learning-based methods. GeoPTH provides a lightweight, non-learning solution that maps trajectories to binary codes by vector-quantizing against geometric prototypes and using the Hausdorff distance , yielding codes of length . By concatenating -bit sub-hashes, GeoPTH achieves competitive accuracy with traditional metrics and learning-based methods while delivering orders-of-magnitude efficiency gains. The approach is robust to noise via prototype ensembles and benefits from the metric properties of , enabling scalable, fast retrieval on large trajectory collections. Future work could explore smarter prototype selection and integration of temporal or semantic cues to capture richer category information.

Abstract

Trajectory similarity retrieval is an important part of spatiotemporal data mining, however, existing methods have the following limitations: traditional metrics are computationally expensive, while learning-based methods suffer from substantial training costs and potential instability. This paper addresses these problems by proposing Geometric Prototype Trajectory Hashing (GeoPTH), a novel, lightweight, and non-learning framework for efficient category-based trajectory retrieval. GeoPTH constructs data-dependent hash functions by using representative trajectory prototypes, i.e., small point sets preserving geometric characteristics, as anchors. The hashing process is efficient, which involves mapping a new trajectory to its closest prototype via a robust, Hausdorff metric. Extensive experiments show that GeoPTH's retrieval accuracy is highly competitive with both traditional metrics and state-of-the-art learning methods, and it significantly outperforms binary codes generated through simple binarization of the learned embeddings. Critically, GeoPTH consistently outperforms all competitors in terms of efficiency. Our work demonstrates that a lightweight, prototype-centric approach offers a practical and powerful alternative, achieving an exceptional retrieval performance and computational efficiency.

Paper Structure

This paper contains 20 sections, 1 theorem, 5 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. The Proposed Framework
  4. Insight: Geometric Proxy for Trajectory Categories
  5. The GeoPTH Framework: A Vector Quantization Approach
  6. Prototype Codebooks Construction
  7. Minimum Distance Quantization
  8. Experiment
  9. Experimental Setup
  10. Datasets
  11. Baselines
  12. Evaluation Protocol
  13. Experimental Results
  14. Comparison with Traditional Baseline Metrics
  15. Comparison with Learning-based Measures
  16. ...and 5 more sections

Key Result

Lemma 1

hausdorff The Hausdorff distance$d_H$ is a metric on the set of non-empty compact subsets of a metric space. As such, it satisfies the triangle inequality: for any three non-empty compact sets X, Y, and Z, we have $d_H(X, Z) \le d_H(X, Y) + d_H(Y, Z)$.

Figures (3)

  • Figure 1: Behavior trajectories from three different users in the Gowalla dataset.
  • Figure 2: An illustration of the GeoPTH framework. A given query trajectory $\mathcal{T}'$ is processed by $M$ independent quantizers. For each quantizer $m$, $\mathcal{T}'$ is compared against all prototypes in its corresponding codebook $Q_m$, and assigned to the index of the prototype with the minimum Hausdorff distance ($d_H$). The resulting $M$ indices are then converted to their binary representations and concatenated to produce the final binary code $\mathcal{H}(\mathcal{T}')$.
  • Figure 3: Parameter analysis of GeoPTH on the Gowalla and Geolife dataset. The results correspond to the code length of $L=64$.

Theorems & Definitions (4)

  • DEFINITION 1: Trajectory
  • DEFINITION 2: Hamming similarity
  • DEFINITION 3: Category-based trajectory hashing retrieval
  • Lemma 1