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Fast rates for empirical vector quantization. (English) Zbl 1349.62038
Summary: We consider the rate of convergence of the expected loss of empirically optimal vector quantizers. Earlier results show that the mean-squared expected distortion for any fixed probability distribution supported on a bounded set and satisfying some regularity conditions decreases at the rate $$\mathcal{O}(\log n/n)$$. We prove that this rate is actually $$\mathcal{O}(1/n)$$. Although these conditions are hard to check, we show that well-clustered distributions with continuous densities supported on a bounded set are included in the scope of this result.

##### MSC:
 62E17 Approximations to statistical distributions (nonasymptotic) 62H30 Classification and discrimination; cluster analysis (statistical aspects)
##### Keywords:
quantization; clustering; localization; fast rates
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##### References:
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