Differentially Private Algorithms for Clustering with Stability Assumptions

TL;DR

This paper introduces a simpler differentially private clustering algorithm for stable inputs, improving utility analysis and extending to k-median and local privacy models, advancing the understanding of private clustering in stable instances.

Contribution

It presents a novel, simpler algorithm for differentially private clustering of stable inputs, with improved utility analysis and broader applicability.

Findings

Algorithm achieves better utility bounds for stable instances.

Extends to k-median and local differential privacy models.

Simplifies previous frameworks by avoiding sample-and-aggregate.

Abstract

We study the problem of differentially private clustering under input-stability assumptions. Despite the ever-growing volume of works on differential privacy in general and differentially private clustering in particular, only three works (Nissim et al. 2007, Wang et al. 2015, Huang et al. 2018) looked at the problem of privately clustering "nice" k-means instances, all three relying on the sample-and-aggregate framework and all three measuring utility in terms of Wasserstein distance between the true cluster centers and the centers returned by the private algorithm. In this work we improve upon this line of works on multiple axes. We present a far simpler algorithm for clustering stable inputs (not relying on the sample-and-aggregate framework), and analyze its utility in both the Wasserstein distance and the k-means cost. Moreover, our algorithm has straight-forward analogues for "nice" k-median instances and for the local-model of differential privacy.