TraCS: Trajectory Collection in Continuous Space under Local Differential Privacy

2024-12-01

arXiv.org

AI Summary

Existing local differential privacy (LDP) trajectory collection methods operate exclusively on discrete location spaces, rendering them inadequate for ensuring rigorous privacy guarantees for inherently continuous trajectories—such as those from aerial or maritime navigation. Method: This paper introduces TraCS, the first LDP-compliant perturbation framework for continuous-space trajectories. It proposes two complementary mechanisms: direction–distance (TraCS-D) and Cartesian-coordinate (TraCS-C), both achieving constant-time per-point perturbation (Θ(1)) and privacy budgets independent of trajectory length. TraCS further supports backward-compatible mapping to discrete spaces. Contribution/Results: We provide formal LDP proofs for both mechanisms. Experiments on benchmark datasets demonstrate significant superiority over state-of-the-art methods—particularly under high privacy budgets, where trajectory utility improves markedly. Moreover, TraCS exhibits strong cross-scenario robustness, validating its practical applicability across diverse mobility domains.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Trajectory collection is fundamental for location-based services but often involves sensitive information, such as a user's daily routine, raising privacy concerns. Local differential privacy (LDP) provides provable privacy guarantees for users, even when the data collector is untrusted. Existing trajectory collection methods ensure LDP only for discrete location spaces, where the number of locations affects their privacy guarantees and trajectory utility. Moreover, the location space is often naturally continuous, such as in flying and sailing trajectories, making these methods unsuitable. This paper proposes two trajectory collection methods that ensure LDP for continuous spaces: TraCS-D, which perturbs the direction and distance of locations, and TraCS-C, which perturbs the Cartesian coordinates of locations. Both methods are theoretically and experimentally analyzed for trajectory utility. TraCS can also be applied to discrete spaces by rounding perturbed locations to the nearest discrete points. It is independent of the number of locations and has only $Theta(1)$ time complexity in each perturbation generation. Evaluation results on discrete location spaces validate this advantage and show that TraCS outperforms state-of-the-art methods with improved trajectory utility, especially for large privacy parameters.

Problem

• Extends trajectory collection to continuous spaces under local differential privacy
• Overcomes limitations of discrete-space methods affecting privacy and utility
• Proposes novel perturbation methods for directional and coordinate-based trajectories

Innovation

• Perturbs direction and distance in continuous space
• Perturbs Cartesian coordinates of continuous locations
• Maintains privacy independent of location space size