Differentially-Private Sublinear-Time Clustering

TL;DR

This paper introduces sublinear-time differentially-private clustering algorithms by combining existing sublinear clustering methods with privacy-preserving techniques, enabling efficient and private unsupervised learning.

Contribution

It presents the first sublinear-time differentially-private clustering algorithms for k-means and k-median, leveraging subsampling and analyzing privacy benefits.

Findings

Achieves sublinear-time private clustering algorithms.

Demonstrates privacy benefits of subsampling for group privacy.

Extends prior work by combining sublinear algorithms with differential privacy.

Abstract

Clustering is an essential primitive in unsupervised machine learning. We bring forth the problem of sublinear-time differentially-private clustering as a natural and well-motivated direction of research. We combine the $k$-means and $k$-median sublinear-time results of Mishra et al. (SODA, 2001) and of Czumaj and Sohler (Rand. Struct. and Algorithms, 2007) with recent results on private clustering of Balcan et al. (ICML 2017), Gupta et al. (SODA, 2010) and Ghazi et al. (NeurIPS, 2020) to obtain sublinear-time private $k$-means and $k$-median algorithms via subsampling. We also investigate the privacy benefits of subsampling for group privacy.