Distributed and Provably Good Seedings for k-Means in Constant Rounds
Olivier Bachem, Mario Lucic, Andreas Krause
Abstract
The k-Means++ algorithm is the state of the art algorithm to solve k-Means clustering problems as the computed clusterings are O(log k) competitive in expectation. However, its seeding step requires k inherently sequential passes through the full data set making it hard to scale to massive data sets. The standard remedy is to use the k-Means|| algorithm which reduces the number of sequential rounds and is thus suitable for a distributed setting. In this paper, we provide a novel analysis of the k-Means|| algorithm that bounds the expected solution quality for any number of rounds and oversampling factors greater than k, the two parameters one needs to choose in practice. In particular, we show that k-Means|| provides
BibTeX
@InProceedings{pmlr-v70-bachem17b,
title = {Distributed and Provably Good Seedings for k-Means in Constant Rounds},
author = {Olivier Bachem and Mario Lucic and Andreas Krause},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {292--300},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/bachem17b/bachem17b.pdf},
url = {https://proceedings.mlr.press/v70/bachem17b.html},
abstract = {The k-Means++ algorithm is the state of the art algorithm to solve k-Means clustering problems as the computed clusterings are O(log k) competitive in expectation. However, its seeding step requires k inherently sequential passes through the full data set making it hard to scale to massive data sets. The standard remedy is to use the k-Means|| algorithm which reduces the number of sequential rounds and is thus suitable for a distributed setting. In this paper, we provide a novel analysis of the k-Means|| algorithm that bounds the expected solution quality for any number of rounds and oversampling factors greater than k, the two parameters one needs to choose in practice. In particular, we show that k-Means|| provides