Quantization/clustering: when and why does k-means work?

Clément Levrard

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arXiv · 1801.03742

Quantization/clustering: when and why does k-means work?

Clément Levrard

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Abstract

Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate how and when these two approaches are compatible. Namely, we show that provided the sample distribution satisfies a margin like condition (in the sense of [27] for supervised learning), both the associated empirical risk minimizer and the output of Lloyd's algorithm provide almost optimal classification in certain cases (in the sense of [6]). Besides, we also show that they achieved fast and optimal convergence rates in terms of sample size and compression risk.

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Clément Levrard. 2018-01-11. Quantization/clustering: when and why does k-means work?. https://arxiv.org/abs/1801.03742

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