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Shock and Vibration
Volume 3, Issue 3, Pages 201-209

A Learning Method for Neural Networks Based on a Pseudoinverse Technique

Chinmoy Pal,1 Ichiro Hagiwara,1 Naoki Kayaba,2 and Shin Morishita2

1Nissan Motor Corporation Research Center, Natsushima-cho, Yokosuka 237, Japan
2Yokohama National University, Dept. of Naval Architecture and Ocean Engineering, 156 Tokiwadai, Hodogaya-ku, Yokohama 240, Japan

Received 1 August 1995; Accepted 14 December 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A theoretical formulation of a fast learning method based on a pseudoinverse technique is presented. The efficiency and robustness of the method are verified with the help of an Exclusive OR problem and a dynamic system identification of a linear single degree of freedom mass–spring problem. It is observed that, compared with the conventional backpropagation method, the proposed method has a better convergence rate and a higher degree of learning accuracy with a lower equivalent learning coefficient. It is also found that unlike the steepest descent method, the learning capability of which is dependent on the value of the learning coefficient ν, the proposed pseudoinverse based backpropagation algorithm is comparatively robust with respect to its equivalent variable learning coefficient. A combination of the pseudoinverse method and the steepest descent method is proposed for a faster, more accurate learning capability.