Differentially private $k$-means clustering via exponential mechanism and max cover

• URL: http://arxiv.org/abs/2009.01220v1
• Date: Wed, 2 Sep 2020 17:52:54 GMT
• Title: Differentially private $k$-means clustering via exponential mechanism and max cover
• Authors: Anamay Chaturvedi, Huy Nguyen, Eric Xu
• Abstract summary: We introduce a new $(epsilon_p, delta_p)$-differentially private algorithm for the $k$-means clustering problem.
• Score: 6.736814259597673
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a new $(\epsilon_p, \delta_p)$-differentially private algorithm for the $k$-means clustering problem. Given a dataset in Euclidean space, the $k$-means clustering problem requires one to find $k$ points in that space such that the sum of squares of Euclidean distances between each data point and its closest respective point among the $k$ returned is minimised. Although there exist privacy-preserving methods with good theoretical guarantees to solve this problem [Balcan et al., 2017; Kaplan and Stemmer, 2018], in practice it is seen that it is the additive error which dictates the practical performance of these methods. By reducing the problem to a sequence of instances of maximum coverage on a grid, we are able to derive a new method that achieves lower additive error then previous works. For input datasets with cardinality $n$ and diameter $\Delta$, our algorithm has an $O(\Delta^2 (k \log^2 n \log(1/\delta_p)/\epsilon_p + k\sqrt{d \log(1/\delta_p)}/\epsilon_p))$ additive error whilst maintaining constant multiplicative error. We conclude with some experiments and find an improvement over previously implemented work for this problem.

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