Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms

Kh. Sh. Mohamed; Xiong Yan; Y. Sh. Mohammed; Abd-Elmoniem A. Elzain; Habtamu Z. A.; Abdrhaman M. Adam

doi:doi:10.11648/j.ajnna.20160201.11

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Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms

Kh. Sh. Mohamed, Xiong Yan, Y. Sh. Mohammed, Abd-Elmoniem A. Elzain, Habtamu Z. A., Abdrhaman M. Adam

Published in American Journal of Neural Networks and Applications (Volume 2, Issue 1)

Received: 14 March 2016 Accepted: 30 March 2016 Published: 10 May 2016

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Abstract

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.

Published in	American Journal of Neural Networks and Applications (Volume 2, Issue 1)
DOI	10.11648/j.ajnna.20160201.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Convergence, Pi-sigma Network, Online Gradient Method, Inner-penalty, Boundedness

References

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Kh. Sh. Mohamed, Xiong Yan, Y. Sh. Mohammed, Abd-Elmoniem A. Elzain, Habtamu Z. A., et al. (2016). Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms. American Journal of Neural Networks and Applications, 2(1), 1-5. https://doi.org/10.11648/j.ajnna.20160201.11

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ACS Style

Kh. Sh. Mohamed; Xiong Yan; Y. Sh. Mohammed; Abd-Elmoniem A. Elzain; Habtamu Z. A., et al. Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms. Am. J. Neural Netw. Appl. 2016, 2(1), 1-5. doi: 10.11648/j.ajnna.20160201.11

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AMA Style

Kh. Sh. Mohamed, Xiong Yan, Y. Sh. Mohammed, Abd-Elmoniem A. Elzain, Habtamu Z. A., et al. Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms. Am J Neural Netw Appl. 2016;2(1):1-5. doi: 10.11648/j.ajnna.20160201.11

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@article{10.11648/j.ajnna.20160201.11,
  author = {Kh. Sh. Mohamed and Xiong Yan and Y. Sh. Mohammed and Abd-Elmoniem A. Elzain and Habtamu Z. A. and Abdrhaman M. Adam},
  title = {Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms},
  journal = {American Journal of Neural Networks and Applications},
  volume = {2},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ajnna.20160201.11},
  url = {https://doi.org/10.11648/j.ajnna.20160201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajnna.20160201.11},
  abstract = {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.},
 year = {2016}
}

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TY  - JOUR
T1  - Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms
AU  - Kh. Sh. Mohamed
AU  - Xiong Yan
AU  - Y. Sh. Mohammed
AU  - Abd-Elmoniem A. Elzain
AU  - Habtamu Z. A.
AU  - Abdrhaman M. Adam
Y1  - 2016/05/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ajnna.20160201.11
DO  - 10.11648/j.ajnna.20160201.11
T2  - American Journal of Neural Networks and Applications
JF  - American Journal of Neural Networks and Applications
JO  - American Journal of Neural Networks and Applications
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2469-7419
UR  - https://doi.org/10.11648/j.ajnna.20160201.11
AB  - 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.
VL  - 2
IS  - 1
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Kh. Sh. Mohamed, Xiong Yan, Y. Sh. Mohammed, Abd-Elmoniem A. Elzain, Habtamu Z. A., et al. (2016). Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms. American Journal of Neural Networks and Applications, 2(1), 1-5. https://doi.org/10.11648/j.ajnna.20160201.11

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ACS Style

Kh. Sh. Mohamed; Xiong Yan; Y. Sh. Mohammed; Abd-Elmoniem A. Elzain; Habtamu Z. A., et al. Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms. Am. J. Neural Netw. Appl. 2016, 2(1), 1-5. doi: 10.11648/j.ajnna.20160201.11

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AMA Style

Kh. Sh. Mohamed, Xiong Yan, Y. Sh. Mohammed, Abd-Elmoniem A. Elzain, Habtamu Z. A., et al. Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms. Am J Neural Netw Appl. 2016;2(1):1-5. doi: 10.11648/j.ajnna.20160201.11

Copy | Download

@article{10.11648/j.ajnna.20160201.11,
  author = {Kh. Sh. Mohamed and Xiong Yan and Y. Sh. Mohammed and Abd-Elmoniem A. Elzain and Habtamu Z. A. and Abdrhaman M. Adam},
  title = {Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms},
  journal = {American Journal of Neural Networks and Applications},
  volume = {2},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ajnna.20160201.11},
  url = {https://doi.org/10.11648/j.ajnna.20160201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajnna.20160201.11},
  abstract = {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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms
AU  - Kh. Sh. Mohamed
AU  - Xiong Yan
AU  - Y. Sh. Mohammed
AU  - Abd-Elmoniem A. Elzain
AU  - Habtamu Z. A.
AU  - Abdrhaman M. Adam
Y1  - 2016/05/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ajnna.20160201.11
DO  - 10.11648/j.ajnna.20160201.11
T2  - American Journal of Neural Networks and Applications
JF  - American Journal of Neural Networks and Applications
JO  - American Journal of Neural Networks and Applications
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2469-7419
UR  - https://doi.org/10.11648/j.ajnna.20160201.11
AB  - 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.
VL  - 2
IS  - 1
ER  -

Copy | Download