# Protecting Locations with Differential Privacy under Temporal Correlations

arXiv: https://arxiv.org/abs/1410.5919 · HTML: https://mlsanity.com/paper/1410.5919/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2014.

## Built on by (most cited first, 17 of 17)

- [OpBoost: A Vertical Federated Tree Boosting Framework Based on Order-Preserving Desensitization](https://mlsanity.com/paper/2210.01318/) (2022)
- [GeoPointGAN: Synthetic Spatial Data with Local Label Differential Privacy](https://mlsanity.com/paper/2205.08886/) (2022)
- [Privacy-Aware Human Mobility Prediction via Adversarial Networks](https://mlsanity.com/paper/2201.07519/) (2022)
- [Privacy-Aware Adversarial Network in Human Mobility Prediction](https://mlsanity.com/paper/2208.05009/) (2022)
- [FedEmb: A Vertical and Hybrid Federated Learning Algorithm using Network And Feature Embedding Aggregation](https://mlsanity.com/paper/2312.00102/) (2023)
- [GeoLife+: Large-Scale Simulated Trajectory Datasets Calibrated to the GeoLife Dataset](https://mlsanity.com/paper/2410.11853/) (2024)
- [Understanding Disclosure Risk in Differential Privacy with Applications to Noise Calibration and Auditing (Extended Version)](https://mlsanity.com/paper/2603.12142/) (2026)
- [Location Trace Privacy Under Conditional Priors](https://mlsanity.com/paper/2102.11955/) (2021)
- [Privacy Amplification by Subsampling in Time Domain](https://mlsanity.com/paper/2201.04762/) (2022)
- [An Easy-to-use and Robust Approach for the Differentially Private De-Identification of Clinical Textual Documents](https://mlsanity.com/paper/2211.01147/) (2022)
- [Directional Privacy for Deep Learning](https://mlsanity.com/paper/2211.04686/) (2022)
- [PMP: Privacy-Aware Matrix Profile against Sensitive Pattern Inference for Time Series](https://mlsanity.com/paper/2301.01838/) (2023)
- [Analysing Fairness of Privacy-Utility Mobility Models](https://mlsanity.com/paper/2304.06469/) (2023)
- [Deep Privacy Funnel Model: From a Discriminative to a Generative Approach with an Application to Face Recognition](https://mlsanity.com/paper/2404.02696/) (2024)
- [Nonparametric spectral density estimation using interactive mechanisms under local differential privacy](https://mlsanity.com/paper/2504.00919/) (2025)
- [Sub-optimal Learning in Meta-Classifier Attacks: A Study of Membership Inference on Differentially Private Location Aggregates](https://mlsanity.com/paper/2412.20456/) (2024)
- [Interpolation-Based Optimization for Enforcing lp-Norm Metric Differential Privacy in Continuous and Fine-Grained Domains](https://mlsanity.com/paper/2601.09946/) (2026)

## Abstract (arXiv)

Concerns on location privacy frequently arise with the rapid development of GPS enabled devices and location-based applications. While spatial transformation techniques such as location perturbation or generalization have been studied extensively, most techniques rely on syntactic privacy models without rigorous privacy guarantee. Many of them only consider static scenarios or perturb the location at single timestamps without considering temporal correlations of a moving user's locations, and hence are vulnerable to various inference attacks. While differential privacy has been accepted as a standard for privacy protection, applying differential privacy in location based applications presents new challenges, as the protection needs to be enforced on the fly for a single user and needs to incorporate temporal correlations between a user's locations. In this paper, we propose a systematic solution to preserve location privacy with rigorous privacy guarantee. First, we propose a new definition, "δ-location set" based differential privacy, to account for the temporal correlations in location data. Second, we show that the well known ℓ1-norm sensitivity fails to capture the geometric sensitivity in multidimensional space and propose a new notion, sensitivity hull, based on which the error of differential privacy is bounded. Third, to obtain the optimal utility we present a planar isotropic mechanism (PIM) for location perturbation, which is the first mechanism achieving the lower bound of differential privacy. Experiments on real-world datasets also demonstrate that PIM significantly outperforms baseline approaches in data utility.