TY - JOUR
AU - Kenthapadi, Krishnaram
AU - Korolova, Aleksandra
AU - Mironov, Ilya
AU - Mishra, Nina
PY - 2013/08/01
Y2 - 2024/07/20
TI - Privacy via the Johnson-Lindenstrauss Transform
JF - Journal of Privacy and Confidentiality
JA - JPC
VL - 5
IS - 1
SE - Articles
DO - 10.29012/jpc.v5i1.625
UR - https://journalprivacyconfidentiality.org/index.php/jpc/article/view/625
SP -
AB - <p>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.</p>
ER -