Convergence properties and stationary points of a perceptron learning algorithm

Author

Shynk, John J. ; Roy, Sumit

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

78

Issue

10

fYear

1990

fDate

10/1/1990 12:00:00 AM

Firstpage

1599

Lastpage

1604

Abstract

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

Keywords

adaptive systems; convergence of numerical methods; learning systems; neural nets; Gaussian random vector; adaptive algorithm; convergence; least mean square algorithm; neural networks; perceptron learning algorithm; stationary points; Adaptive algorithm; Algorithm design and analysis; Convergence; Feedforward neural networks; Least squares approximation; Multi-layer neural network; Multilayer perceptrons; Neural networks; Neurons; Pattern recognition;

fLanguage

English

Journal_Title

Proceedings of the IEEE

Publisher

ieee

ISSN

0018-9219

Type

jour

DOI

10.1109/5.58345

Filename

58345