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We propose a new algorithm for k-means clustering in a distributed setting,where the data is distributed across many machines, and a coordinatorcommunicates with these machines to calculate the output clustering. Ouralgorithm guarantees a cost approximation factor and a number of communicationrounds that depend only on the computational capacity of the coordinator.Moreover, the algorithm includes a built-in stopping mechanism, which allows itto use fewer communication rounds whenever possible. We show both theoreticallyand empirically that in many natural cases, indeed 1-4 rounds suffice. Incomparison with the popular k-means|| algorithm, our approach allows exploitinga larger coordinator capacity to obtain a smaller number of rounds. Ourexperiments show that the k-means cost obtained by the proposed algorithm isusually better than the cost obtained by k-means||, even when the latter isallowed a larger number of rounds. Moreover, the machine running time in ourapproach is considerably smaller than that of k-means||. Code for running thealgorithm and experiments is available athttps://github.com/selotape/distributed_k_means.

Fast Distributed k-Means with a Small Number of Rounds