Differentially Private Publication of Location Entropy

TL;DR

This paper addresses the challenge of publishing location entropy data with differential privacy, proposing novel sensitivity bounds and techniques to reduce noise while maintaining privacy and data utility.

Contribution

It introduces the first differential privacy framework for location entropy, deriving sensitivity bounds and proposing thresholding and weaker privacy notions for improved utility.

Findings

Thresholding reduces noise significantly.

Extended techniques improve data utility.

Methods preserve data distribution without compromising privacy.

Abstract

Location entropy (LE) is a popular metric for measuring the popularity of various locations (e.g., points-of-interest). Unlike other metrics computed from only the number of (unique) visits to a location, namely frequency, LE also captures the diversity of the users' visits, and is thus more accurate than other metrics. Current solutions for computing LE require full access to the past visits of users to locations, which poses privacy threats. This paper discusses, for the first time, the problem of perturbing location entropy for a set of locations according to differential privacy. The problem is challenging because removing a single user from the dataset will impact multiple records of the database; i.e., all the visits made by that user to various locations. Towards this end, we first derive non-trivial, tight bounds for both local and global sensitivity of LE, and show that to satisfy $\epsilon$-differential privacy, a large amount of noise must be introduced, rendering the published results useless. Hence, we propose a thresholding technique to limit the number of users' visits, which significantly reduces the perturbation error but introduces an approximation error. To achieve better utility, we extend the technique by adopting two weaker notions of privacy: smooth sensitivity (slightly weaker) and crowd-blending (strictly weaker). Extensive experiments on synthetic and real-world datasets show that our proposed techniques preserve original data distribution without compromising location privacy.