Colored Noise Mechanism for Differentially Private Clustering

TL;DR

This paper introduces a novel differentially private mechanism for K-means clustering that optimally adds Gaussian noise, providing privacy guarantees while maintaining accuracy, and demonstrates its effectiveness through analytical solutions and comparisons.

Contribution

It presents an analytical solution for the optimal Gaussian noise covariance in differentially private K-means clustering, improving privacy-utility trade-offs.

Findings

Optimal covariance derived analytically

Outperforms existing privacy mechanisms

Effective privacy preservation with minimal utility loss

Abstract

The goal of this paper is to propose and analyze a differentially private randomized mechanism for the $K$-means query. The goal is to ensure that the information received about the cluster-centroids is differentially private. The method consists in adding Gaussian noise with an optimum covariance. The main result of the paper is the analytical solution for the optimum covariance as a function of the database. Comparisons with the state of the art prove the efficacy of our approach.