$k$-Means Clustering with Distance-Based Privacy

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper


Alessandro Epasto, Vahab Mirrokni, Shyam Narayanan, Peilin Zhong


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.