Convergence of the modified recurrent Perceptron learning rule in Cellular Neural Networks

Abstract

The purpose of the paper is to prove the convergence of the modified Perceptron learning rule in order to apply to all recurrent neural networks in general and to Cellular Neural Networks (CNN) in particular. Cellular Neural Networks are characterized by the saturation function for the output activation function. Based on the saturation function, we define the relation between the Perceptron learning rule and the Least Mean Squares (LMS) algorithms in order to propose theorems and prove the convergence of the Perceptron learning rule. A number of case studies are presented in Lemma 1 and Lemma 2 of the paper. The article also presents a few experiments to verify the convergence of the algorithm by simulation.