Optimal vector quantization in terms of Wasserstein distance |
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Authors: | Wolfgang Kreitmeier |
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Institution: | Wolfgang Kreitmeier, University of Passau, Department of Informatics and Mathematics, D-94032 Passau, Germany |
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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-α-entropy as a complexity constraint, which includes the special case of (Shannon-)entropy constrained (α=1) and memory-size constrained (α=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) 11] and 12]. |
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Keywords: | 60B10 60E05 62E17 68P30 94A17 94A29 |
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