Differential Privacy for Clustering Under Continual Observation

TL;DR

This paper introduces a differentially private clustering algorithm for data that changes over time, achieving low error that scales logarithmically with the number of updates, and extends to k-median clustering.

Contribution

It presents the first approximation algorithm for differentially private clustering under continual observation with logarithmic error dependence on update count.

Findings

Achieves epsilon-differential privacy for dynamic clustering.

Error depends only logarithmically on the number of updates.

Extends results partially to k-median clustering.

Abstract

We consider the problem of clustering privately a dataset in $\mathbb{R}^d$ that undergoes both insertion and deletion of points. Specifically, we give an $\varepsilon$-differentially private clustering mechanism for the $k$-means objective under continual observation. This is the first approximation algorithm for that problem with an additive error that depends only logarithmically in the number $T$ of updates. The multiplicative error is almost the same as non privately. To do so we show how to perform dimension reduction under continual observation and combine it with a differentially private greedy approximation algorithm for $k$-means. We also partially extend our results to the $k$-median problem.