Quantization and classification - Quantification et classification

Quantization and classification

Quantification et classification

Robert M. Gray

Information Systems Laboratory, Department of Electrical Engineering, Stanford, CA 94305

Page: 
513-518
|
Received: 
19 March 1998
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

The problem of quantizer design for detection or classification has a long history, with classical contributions by Kassam, Poor, Picinbono, Bucklew and others. The goal was to design a quantizer such that a detection rule based on the quantized information was optimized. During recent years an alternative approach has been developed which seeks to jointly optimize quantization and classification by incorporating the Bayes risk resulting from the quantizer into the quantizer optimization. In this paper the general classical approach of Picinbono and Duvaut is compared contrasted with the joint approach and illustrated by a simple example.

Résumé

Il existe une importante littérature traitant du problème de la conception d'un quantificateur pour un système de détection ou de classification. A l'origine, les travaux menés dans ce domaine - notamment par Kassam, Poor, Picinbono et Bucklew - ont pour but de concevoir un quantificateur qui optimise une règle de décision basée sur l'information quantifiée. Rompant avec cette approche classique, ces dernières années ont vu l'émergence d'une approche alternative dont l'objectif est d'optimiser conjointement les opérations de quantification et de classification. L'optimisation conjointe est réalisée par minimisation d'un critère Lagrangien comprennant l'erreur quadratique moyenne (quantification) et le risque de Bayes (classification). Dans cet article, nous proposons de comparer l'approche conjointe à l'approche classique, plus courante, de Picinbono et Duvaut . Nous illustrons les deux méthodes à l'aide d'un exemple simple.

Keywords: 

Quantification, détection, classification, classification optimale par risque de Bayes, estimation de densité

Mots clés

Signal quantization, signal detection, optimal classification, density estimation

1. Introduction
2. Bayes Vector Quantization
3. Optimality Properties of Bayes VQ
4. BVQ and Density Estimation
5. Kohonen's Example
  References

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