Differentially Private k-Means with Constant Multiplicative Error

TL;DR

This paper introduces new differentially private algorithms for the Euclidean k-means problem that achieve constant multiplicative error, improving error guarantees and reducing interaction rounds in the local model.

Contribution

It presents the first efficient private algorithms for k-means with constant multiplicative error in both centralized and local differential privacy models.

Findings

Achieves significantly improved error guarantees over previous methods.

Reduces the number of interaction rounds in the local model.

Provides private algorithms for computing corsets in k-means clustering.

Abstract

We design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error guarantees than the previous state-of-the-art. In addition, in the local model, our algorithm significantly reduces the number of interaction rounds. Although the problem has been widely studied in the context of differential privacy, all of the existing constructions achieve only super constant approximation factors. We present, for the first time, efficient private algorithms for the problem with constant multiplicative error. Furthermore, we show how to modify our algorithms so they compute private corsets for k-means clustering in both models.