Stationary points and performance surfaces of a perceptron learning algorithm for a nonseparable data model

A single-layer perceptron divides the input signal space into two regions separated by a hyperplane. In many applications, the training signal of the adaptive algorithm represents more complicated decision regions which usually are not linearly separable. For these cases, a multilayer perceptron is generally needed to adequately partition the signal space and to minimize classification errors. The authors derive the stationary points of Rosenblatt´s learning algorithm for a single-layer perceptron and a nonseparable, two-layer model of the training data. The analysis is based on a system identification formulation of the training signal, and the perceptron input signals are modeled as independent Gaussian sequences. An expression for the corresponding performance function is also derived, and computer simulations are presented that verify the analytical results