Making Old Things New: A Unified Algorithm for Differentially Private Clustering

TL;DR

This paper presents a unified algorithmic framework for differentially private clustering that adapts a 20-year-old algorithm to multiple privacy models, improving and extending previous results, including the continual observation setting.

Contribution

It introduces a unified approach that works across various privacy models, simplifying and enhancing private clustering algorithms.

Findings

Matches almost all previous results in private clustering

Extends to the continual observation privacy model

Provides improvements in certain privacy settings

Abstract

As a staple of data analysis and unsupervised learning, the problem of private clustering has been widely studied under various privacy models. Centralized differential privacy is the first of them, and the problem has also been studied for the local and the shuffle variation. In each case, the goal is to design an algorithm that computes privately a clustering, with the smallest possible error. The study of each variation gave rise to new algorithms: the landscape of private clustering algorithms is therefore quite intricate. In this paper, we show that a 20-year-old algorithm can be slightly modified to work for any of these models. This provides a unified picture: while matching almost all previously known results, it allows us to improve some of them and extend it to a new privacy model, the continual observation setting, where the input is changing over time and the algorithm must output a new solution at each time step.