Differentially Private Clustering via Maximum Coverage

TL;DR

This paper introduces differentially private algorithms for clustering in metric spaces, achieving improved accuracy and flexibility by leveraging existing clustering algorithms as black-boxes.

Contribution

It provides polynomial-time differentially private algorithms for k-medians and k-means with better error bounds and adaptable trade-offs, using black-box clustering methods.

Findings

Polynomial algorithms with constant multiplicative error

Lower additive error than previous methods

Flexible trade-off between runtime and accuracy

Abstract

This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial algorithms with constant multiplicative error and lower additive error than the previous state-of-the-art for each problem. Additionally, our algorithms use a clustering algorithm without differential privacy as a black-box. This allows practitioners to control the trade-off between runtime and approximation factor by choosing a suitable clustering algorithm to use.