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Greedy vector quantization

Abstract : We investigate the greedy version of the L^p-optimal vector quantization problem for an R^d-valued random vector X\in L^p. We show the existence of a sequence (a_N) such that a_N minimizes a\mapsto\big \|\min_{1\le i\le N-1}|X-a_i|\wedge |X-a|\big\|_{p}: the L^p-mean quantization error at level N induced by (a_1,\ldots,a_{N-1},a). We show that this sequence produces L^p-rate optimal N-tuples a^{(N)}=(a_1,\ldots,a_{_N}): their L^p-mean quantization errors at level $N$ go to 0 at rate N^{-\frac 1d}. Greedy optimal sequences also satisfy, under natural additional assumptions, the distortion mismatch property: the N-tuples a^{(N)} remain rate optimal with respect to the L^q-norms, if p\le q
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https://hal.archives-ouvertes.fr/hal-01026116
Contributor : Gilles Pagès <>
Submitted on : Saturday, July 19, 2014 - 6:34:25 PM
Last modification on : Friday, March 27, 2020 - 3:56:39 AM
Document(s) archivé(s) le : Monday, November 24, 2014 - 8:41:17 PM

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  • HAL Id : hal-01026116, version 1

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Harald Luschgy, Gilles Pagès. Greedy vector quantization. 2014. ⟨hal-01026116⟩

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