$k$-Means Clustering with Distance-Based Privacy

Alessandro Epasto, Vahab Mirrokni, Shyam Narayanan, Peilin Zhong

Keywords: differential Privacy, k-means, k-median, clustering, distance-based privacy

TL;DR: We study differentially private k-means with a more recent notion of distance-based privacy. We theoretically and empirically provide better algorithms than previous differentially private k-means algorithms.

Abstract: In this paper, we initiate the study of Euclidean clustering with Distance-based privacy. Distance-based privacy is motivated by the fact that it is often only needed to protect the privacy of exact, rather than approximate, locations. We provide constant-approximate algorithms for $k$-means and $k$-median clustering, with additive error depending only on the attacker's precision bound $\rho$, rather than the radius $\Lambda$ of the space. In addition, we empirically demonstrate that our algorithm performs significantly better than previous differentially private clustering algorithms, as well as naive distance-based private clustering baselines.

Submission Number: 8858