On the convergence behavior of Rosenblatt´s perceptron learning algorithm

A stochastic analysis of the steady-state and transient convergence properties of a single-layer perceptron is presented. The training data are modeled using a system identification formulation with Gaussian inputs, and the perceptron weights are adjusted by Rosenblatt´s learning algorithm. It is shown that the convergence points of the algorithm depend on the step size μ and the input signal power σ_x². Two coupled nonlinear recursions that describe the transient behavior of the algorithm are derived. Computer simulations that verify the analytical models are also presented