Approximation of the gradient of the error probability for vector quantizers

Vector Quantizers (VQ) can be exploited for classification. In particular the gradient of the error probability performed by a VQ with respect to the position of its code vectors can be formally derived, hence the optimum VQ can be theoretically found. Unfortunately, this equation is of limited use in practice, since it relies on the knowledge of the class conditional probability distributions. In order to apply the method to real problems where distributions are unknown, a stochastic approximation has been previously proposed to derive a practical learning algorithm. In this paper we relax some of the assumptions underlying the original proposal and study the advantages of the resulting algorithm by both synthetic and real case studies.