A NEURAL NETWORK APPROACH TO STATISTICAL PATTERN-CLASSIFICATION BY SEMIPARAMETRIC ESTIMATION OF PROBABILITY DENSITY-FUNCTIONS

The paper outlines a method for designing near optimal nonlinear classifiers based on a self-organizing technique for estimating probability density functions when only weak assumptions are made about the densities. The classical parametric and nonparametric methods for estimating density functions have a number of drawbacks; parametric methods give weak results on unknown distributions, while nonparametric methods require extensive amounts of design samples, storage capacity, and computing power. The present method avoids these disadvantages by parameterizing a set of component densities from which the actual densities are constructed. The parameters of the component densities are optimized by a self-organizing algorithm, reducing to a minimum the labeling of design samples. All the required computations are realized with the simple "sum of product" units commonly used in connectionist models. The density approximations produced by the method are illustrated in two dimensions for a multispectral image classification task. The practical use of the method is illustrated by a small speech recognition problem, that of recognizing 18 Swedish consonants. Related issues of invariant projections, cross-class pooling of data, and subspace partitioning are also discussed.