Locally private k-means clustering

Uri Stemmer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

27 Scopus citations


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 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 . We show that the additive error we obtain is almost optimal in terms of its dependency in the database size n. Specifically, we give a simple lower bound showing that every locally-private algorithm for the k-means must have additive error at least ≈ √n.

Original languageEnglish
Title of host publication31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
EditorsShuchi Chawla
PublisherAssociation for Computing Machinery
Number of pages12
ISBN (Electronic)9781611975994
StatePublished - 1 Jan 2020
Externally publishedYes
Event31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States
Duration: 5 Jan 20208 Jan 2020

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Country/TerritoryUnited States
CitySalt Lake City

ASJC Scopus subject areas

  • Software
  • General Mathematics


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