Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms
American Journal of Neural Networks and Applications
Volume 2, Issue 1, February 2016, Pages: 1-5
Received: Mar. 14, 2016;
Accepted: Mar. 30, 2016;
Published: May 10, 2016
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Kh. Sh. Mohamed, Mathematical Department, College of Science, Dalanj University, Dalanj, Sudan; School of Mathematical Sciences, Dalian University of Technology, Dalian, China
Xiong Yan, School of Science, Liaoning University of Science & Technology, Anshan, China
Y. Sh. Mohammed, Physics Department, College of Education, Dalanj University, Dalanj, Sudan; Department of Physics, College of Science & Art, Qassim University, Oklat Al- Skoor, Saudi Arabia
Abd-Elmoniem A. Elzain, Department of Physics, College of Science & Art, Qassim University, Oklat Al- Skoor, Saudi Arabia; Department Department of Physics, University of Kassala, Kassala, Sudan
Habtamu Z. A., School of Mathematical Sciences, Dalian University of Technology, Dalian, China
Abdrhaman M. Adam, School of Mathematical Sciences, Dalian University of Technology, Dalian, China
This paper investigates an online gradient method with inner- penalty for a novel feed forward network it is called pi-sigma network. This network utilizes product cells as the output units to indirectly incorporate the capabilities of higher-order networks while using a fewer number of weights and processing units. Penalty term methods have been widely used to improve the generalization performance of feed forward neural networks and to control the magnitude of the network weights. The monotonicity of the error function and weight boundedness with inner- penalty term and both weak and strong convergence theorems in the training iteration are proved.
Kh. Sh. Mohamed,
Y. Sh. Mohammed,
Abd-Elmoniem A. Elzain,
Habtamu Z. A.,
Abdrhaman M. Adam,
Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms, American Journal of Neural Networks and Applications.
Vol. 2, No. 1,
2016, pp. 1-5.
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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