A Gradient Descent VQ Classification Algorithm

Abstract

Vector Quantization (VQ) has its origins in signal processing where it is used for compact, accurate representation of input signals. However, since VQ induces a partitioning of the input space, it can also be used for statistical pattern recognition. In this paper we present a novel gradient descent VQ classification algorithm which minimizes the Bayes Risk, which we refer to as the Generalized Bayes Risk VQ (GBRVQ), and compare its performance to other VQ classification algorithms. I. Introduction Vector quantization (VQ), a generalization of the quantization of scalars to vectors [1], is the approximation of points (vectors) in a continuous input space by a finite number of representative vectors in the same input space. The basic definition of a vector quantizer is as follows: Definition I.1 (Vector Quantizer) A K-level, n-dimensional vector quantizer, Q is a mapping, Q : IR n ! C, from an n-dimensional Euclidean space, IR n into a finite set C = fw 1 ; w 2 ; \Delta \Delta \D..