Optimal vector quantization in terms of Wasserstein distance

Wolfgang Kreitmeier

Journal of Multivariate Analysis, 2011, vol. 102, issue 8, 1225-1239

Abstract: The optimal quantizer in memory-size constrained vector quantization induces a quantization error which is equal to a Wasserstein distortion. However, for the optimal (Shannon-)entropy constrained quantization error a proof for a similar identity is still missing. Relying on principal results of the optimal mass transportation theory, we will prove that the optimal quantization error is equal to a Wasserstein distance. Since we will state the quantization problem in a very general setting, our approach includes the Rényi-[alpha]-entropy as a complexity constraint, which includes the special case of (Shannon-)entropy constrained ([alpha]=1) and memory-size constrained ([alpha]=0) quantization. Additionally, we will derive for certain distance functions codecell convexity for quantizers with a finite codebook. Using other methods, this regularity in codecell geometry has already been proved earlier by György and Linder (2002, 2003)Â [11] and [12].

Keywords: Wasserstein; distance; Optimal; quantization; error; Codecell; convexity; Renyi-[alpha]-entropy (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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