Distributed and Provably Good Seedings for kMeans in Constant Rounds
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:292300, 2017.
Abstract
The kMeans++ algorithm is the state of the art algorithm to solve kMeans 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 kMeans 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 kMeans 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 kMeans provides provably good clusterings even for a small, constant number of iterations. This theoretical finding explains the common observation that kMeans performs extremely well in practice even if the number of rounds is low. We further provide a hard instance that shows that an additive error term as encountered in our analysis is inevitable if less than k1 rounds are employed.
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