## Abstract

We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees a cost approximation factor and a number of communication rounds that depend only on the computational capacity of the coordinator. Moreover, the algorithm includes a built-in stopping mechanism, which allows it to use fewer communication rounds whenever possible. We show both theoretically and empirically that in many natural cases, indeed 1-4 rounds suffice. In comparison with the popular k-means|| algorithm, our approach allows exploiting a larger coordinator capacity to obtain a smaller number of rounds. Our experiments show that the k-means cost obtained by the proposed algorithm is usually better than the cost obtained by k-means||, even when the latter is allowed a larger number of rounds. Moreover, the machine running time in our approach is considerably smaller than that of k-means||. Code for running the algorithm and experiments is available at https://github.com/selotape/distributed_k_means.

Original language | English |
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Pages (from-to) | 850-874 |

Number of pages | 25 |

Journal | Proceedings of Machine Learning Research |

Volume | 206 |

State | Published - 1 Jan 2023 |

Event | 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain Duration: 25 Apr 2023 → 27 Apr 2023 |

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability