Fast Distributed k-Means with a Small Number of Rounds
Tom Hess, Ron Visbord, Sivan Sabato
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$||$.
BibTeX
@InProceedings{pmlr-v206-hess23a,
title = {Fast Distributed k-Means with a Small Number of Rounds},
author = {Hess, Tom and Visbord, Ron and Sabato, Sivan},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {850--874},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/hess23a/hess23a.pdf},
url = {https://proceedings.mlr.press/v206/hess23a.html},
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$||$.}
}