Abstract
We design a new algorithm for the Euclidean k-means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the k-means objective incur both additive and multiplicative errors. Our algorithm significantly reduces the additive error while keeping the multiplicative error the same as in previous state-of-the-art results. Specifically, on a database of size n, our algorithm guarantees O(1) multiplicative error and ≈ n1=2+a additive error for an arbitrarily small constant a > 0. All previous algorithms in the local model had additive error ≈ n2=3+a. Our techniques extend to k-median clustering. We show that the additive error we obtain is almost optimal in terms of its dependency on the database size n. Specifically, we give a simple lower bound showing that every locally-private algorithm for the k-means objective must have additive error at least ≈ √ n.
Original language | English |
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Journal | Journal of Machine Learning Research |
Volume | 22 |
State | Published - 1 May 2021 |
Keywords
- Clustering
- Differential privacy
- K-means
- K-median
- Local model
All Science Journal Classification (ASJC) codes
- Software
- Artificial Intelligence
- Control and Systems Engineering
- Statistics and Probability