Protecting Locations with Differential Privacy under Temporal Correlations

TL;DR

This paper introduces a new differential privacy framework for location data that accounts for temporal correlations, proposing a novel sensitivity measure and an optimal perturbation mechanism to enhance privacy without sacrificing utility.

Contribution

It presents a new $oldsymbol{ ext{ extdelta}}$-location set differential privacy definition, a sensitivity hull concept, and the planar isotropic mechanism for optimal location perturbation.

Findings

PIM outperforms baseline methods in data utility.

The sensitivity hull effectively bounds differential privacy error.

The approach provides rigorous privacy guarantees considering temporal correlations.

Abstract

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, "$\delta$-location set" based differential privacy, to account for the temporal correlations in location data. Second, we show that the well known $\ell_1$-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.