Privacy via the Johnson-Lindenstrauss Transform

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.

24 pages

References in corpus (1)

• A Sparse Johnson--Lindenstrauss Transform

Cited by in corpus (22)

• RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response
• MVG Mechanism: Differential Privacy under Matrix-Valued Query
• Learning Privately over Distributed Features: An ADMM Sharing Approach
• Differentially-Private "Draw and Discard" Machine Learning
• A Random Matrix Approach to Differential Privacy and Structure Preserved Social Network Graph Publishing
• Privacy-Utility Trade-off of Linear Regression under Random Projections and Additive Noise
• Randomness Efficient Fast-Johnson-Lindenstrauss Transform with Applications in Differential Privacy and Compressed Sensing
• Facebook's Advertising Platform: New Attack Vectors and the Need for Interventions
• Sub-Linear Privacy-Preserving Near-Neighbor Search
• Preserving Differential Privacy Between Features in Distributed Estimation
• Arrays of (locality-sensitive) Count Estimators (ACE): High-Speed Anomaly Detection via Cache Lookups
• Improved Differentially Private Euclidean Distance Approximation
• Efficient Differentially Private $F_0$ Linear Sketching
• Investigating Privacy Leakage in Dimensionality Reduction Methods via Reconstruction Attack
• Matrix Sketching for Secure Collaborative Machine Learning
• Utility Preserving Secure Private Data Release
• On The Differential Privacy of Thompson Sampling With Gaussian Prior
• A Differential Privacy Mechanism Design Under Matrix-Valued Query
• PrivateMail: Supervised Manifold Learning of Deep Features With Differential Privacy for Image Retrieval
• DP-CDA: An Algorithm for Enhanced Privacy Preservation in Dataset Synthesis Through Randomized Mixing
• An Introduction to Johnson-Lindenstrauss Transforms
• STORM: Foundations of End-to-End Empirical Risk Minimization on the Edge