Topology Preserving Maps

Abstract

This chapter introduces three negative feedback artificial neural network architectures which perform a vector quantization. Vector quantization is used in signal processing applications to encode a high-dimensional signal in order to minimise processing/transmission costs. The basic aim is to associate with each group of vectors of the raw data a code which uniquely identifies that group. If the vectors of the group are sufficiently alike and the decoded code is sufficiently representative of the group, then the error when the code is used to represent a vector in the group can be made acceptably small. One further feature of the mapping which we desire is that it should retain an accurate representation of the topology of the data space. This is a rather complex feature to specify absolutely accurately so we shall initially content ourselves with a mapping in which nearby points in the data space are mapped to the same or nearby neurons in the coding space while ensuring that nearby neurons in the coding space are decoded to nearby points in data space.