On the behavior of a VQ algorithm

Vector quantization algorithms have long been used to find a finite set of exemplars which represent a data set to within an a priori error tolerance. Such a representation is essential in codebook based data compression and transmission. This study is motivated by the application where the data to be encoded consists of subclasses. The codebook must provide information compression within the several subclasses, however, minimization of interclass errors is of equal importance. In an earlier study Abou-Ali and Porter (see Proc. IEEE Aerospace Conf., 1997) presented modifications to a basic VQ algorithm which adapts it to the multiclass vector quantizing setting. We also explore the behavior of the modified algorithm on selected benchmark applications. It was demonstrated, in particular, that overlapping subclasses can be accommodated by the algorithm. We present an analytic analysis of the multiclass VQ algorithm introduced by Abou-Ali et al. We show that the border pairs between classes act in concert to separate the classes while providing vector quantization to the union of sets. The movement of border pairs is also related to the classic Ho-Kashyap algorithm for constructing separating hyperplanes.