Differentially Private Clustering in Data Streams

TL;DR

This paper introduces the first differentially private algorithms for streaming $k$-means and $k$-median clustering, achieving sublinear space complexity and providing strong approximation guarantees while preserving data privacy.

Contribution

It presents novel differentially private streaming clustering algorithms with provable approximation guarantees and space efficiency, utilizing a new framework based on offline DP coresets.

Findings

Achieves $O(1)$-multiplicative approximation with sublinear space.

Provides $(1+eta)$-multiplicative approximation with adjustable space complexity.

Offers algorithms with polylogarithmic dependence on stream length $T$.

Abstract

Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central concern in many real-world applications, non-private clustering algorithms may not be as applicable in many scenarios. In this work, we provide the first differentially private algorithms for $k$-means and $k$-median clustering of $d$-dimensional Euclidean data points over a stream with length at most $T$ using space that is sublinear (in $T$) in the continual release setting where the algorithm is required to output a clustering at every timestep. We achieve (1) an $O(1)$-multiplicative approximation with $\tilde{O}(k^{1.5} \cdot poly(d,\log(T)))$ space and $poly(k,d,\log(T))$ additive error, or (2) a $(1+\gamma)$-multiplicative approximation with $\tilde{O}_\gamma(poly(k,2^{O_\gamma(d)},\log(T)))$ space for any $\gamma>0$, and the additive error is $poly(k,2^{O_\gamma(d)},\log(T))$. Our main technical contribution is a differentially private clustering framework for data streams which only requires an offline DP coreset or clustering algorithm as a blackbox.