Differential Privacy for Clustering Under Continual Observation

• URL: http://arxiv.org/abs/2307.03430v2
• Date: Thu, 27 Jul 2023 14:36:29 GMT
• Title: Differential Privacy for Clustering Under Continual Observation
• Authors: Max Dupr\'e la Tour, Monika Henzinger, David Saulpic
• Abstract summary: We consider the problem of clustering privately a dataset in $mathbbRd$ that undergoes both insertion and deletion of points. We give an $varepsilon$-differentially private clustering mechanism for the $k$-means objective under continual observation.
• Score: 5.220940151628734
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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