Fast and Provably Good Seedings for k-Means

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Authors

Olivier Bachem, Mario Lucic, Hamed Hassani, Andreas Krause

Abstract

<p>Seeding - the task of finding initial cluster centers - is critical in obtaining high-quality clusterings for k-Means. However, k-means++ seeding, the state of the art algorithm, does not scale well to massive datasets as it is inherently sequential and requires k full passes through the data. It was recently shown that Markov chain Monte Carlo sampling can be used to efficiently approximate the seeding step of k-means++. However, this result requires assumptions on the data generating distribution. We propose a simple yet fast seeding algorithm that produces <em>provably</em> good clusterings even <em>without assumptions</em> on the data. Our analysis shows that the algorithm allows for a favourable trade-off between solution quality and computational cost, speeding up k-means++ seeding by up to several orders of magnitude. We validate our theoretical results in extensive experiments on a variety of real-world data sets.</p>