Convergence properties and stationary points of a perceptron learning algorithm

An analysis of the stationary (convergence) points of an adaptive algorithm that adjusts the perceptron weights is presented. This algorithm is identical in form to the least-mean-square (LMS) algorithm, except that a hard limiter is incorporated at the output of the summer. The algorithm is described in detail, a simple two-input example is presented, and some of its convergence properties are illustrated. When the input of the perceptron is a Gaussian random vector, the stationary points of the algorithm are not unique and they depend on the algorithm step size and the momentum constant. The stationary points of the algorithm are presented, and the properties of the adaptive weight vector near convergence are discussed. Computer simulations that verify the analysis are given