Conditions for Convergence of the Normalized LMS Algorithm in Neural Learning.
Kazushi Ikeda, Seiji Miyoshi, Kenji Nakayama · The Brain & Neural Networks · 1997
The Perceptron Learning algorithm for linear dichotomy can be regarded as the LMS algorithm which is one of the most popular algorithms for transversal filters. The Normalized LMS (N-LMS) algorithm is one of the improved versions of the LMS algorithm for transversal filters and we apply it to linear dichotomies. In this paper, the proof of the convergence of the N-LMS algorithm for linear dichotomies in a finite number of iterations when the learning coefficient μ is unity, and a sufficient condition of μ for the convergence are given.