A Three-Layered Perception for K-L Transformation

Abstract

This paper proposes a three-layerred perceptron for Karhunen-Loeve transformation . The perceptron has the same number N of input units as input variable dimensions, R(≦N) hidden units and R columns of N output-units with unilateral summing networks between adjacent columns. This paper also clarifies theoretically that the perceptron extracts the dominant R components of K-L transform of each input-sample through its hidden unit-outputs after learning for identity-mapping between the input layer and each output-column. Simulations demonstrate exact transformations and rapid learning performances for various kinds of input samples.