Privacy via the Johnson-Lindenstrauss Transform

TL;DR

This paper presents a method combining Johnson-Lindenstrauss projections and Gaussian noise to enable privacy-preserving distance estimation between users' data vectors, balancing data utility and privacy.

Contribution

It introduces a novel approach using sparse Johnson-Lindenstrauss transforms with noise addition to achieve differential privacy for distance computations.

Findings

The method preserves differential privacy with adjustable noise levels.

It allows accurate distance approximation from perturbed, lower-dimensional data.

Comparison with other perturbation techniques highlights its effectiveness.

Abstract

Suppose that party A collects private information about its users, where each user's data is represented as a bit vector. Suppose that party B has a proprietary data mining algorithm that requires estimating the distance between users, such as clustering or nearest neighbors. We ask if it is possible for party A to publish some information about each user so that B can estimate the distance between users without being able to infer any private bit of a user. Our method involves projecting each user's representation into a random, lower-dimensional space via a sparse Johnson-Lindenstrauss transform and then adding Gaussian noise to each entry of the lower-dimensional representation. We show that the method preserves differential privacy---where the more privacy is desired, the larger the variance of the Gaussian noise. Further, we show how to approximate the true distances between users via only the lower-dimensional, perturbed data. Finally, we consider other perturbation methods such as randomized response and draw comparisons to sketch-based methods. While the goal of releasing user-specific data to third parties is more broad than preserving distances, this work shows that distance computations with privacy is an achievable goal.