Differentially Private k-Means via Exponential Mechanism and Max Cover

Authors

  • Huy L. Nguyen Northeastern University
  • Anamay Chaturvedi Northeastern University
  • Eric Z Xu Northeastern University

Keywords:

Clustering, Optimization, Privacy & Security

Abstract

We introduce a new (ϵₚ, δₚ)-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, 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 than previous works. For input datasets with cardinality n and diameter Δ, our algorithm has an O(Δ² (k log² n log(1/δₚ)/ϵₚ + k √(d log(1/δₚ))/ϵₚ)) 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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Published

2021-05-18

How to Cite

Nguyen, H. L., Chaturvedi, A., & Xu, E. Z. (2021). Differentially Private k-Means via Exponential Mechanism and Max Cover. Proceedings of the AAAI Conference on Artificial Intelligence, 35(10), 9101-9108. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/17099

Issue

Section

AAAI Technical Track on Machine Learning III