Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks
The online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the mo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/829692 |
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| _version_ | 1850167596748374016 |
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| author | Huisheng Zhang Dongpo Xu Zhiping Wang |
| author_facet | Huisheng Zhang Dongpo Xu Zhiping Wang |
| author_sort | Huisheng Zhang |
| collection | DOAJ |
| description | The online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the monotonicity of the error function, it is proved that the gradient of the error function tends to zero and the weight sequence tends to a fixed point. A numerical example is given to support the theoretical findings. |
| format | Article |
| id | doaj-art-e7ac1d13c961490780d884297ee812c7 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e7ac1d13c961490780d884297ee812c72025-08-20T02:21:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/829692829692Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural NetworksHuisheng Zhang0Dongpo Xu1Zhiping Wang2Department of Mathematics, Dalian Maritime University, Dalian 116026, ChinaDepartment of Applied Mathematics, Harbin Engineering University, Harbin 150001, ChinaDepartment of Mathematics, Dalian Maritime University, Dalian 116026, ChinaThe online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the monotonicity of the error function, it is proved that the gradient of the error function tends to zero and the weight sequence tends to a fixed point. A numerical example is given to support the theoretical findings.http://dx.doi.org/10.1155/2010/829692 |
| spellingShingle | Huisheng Zhang Dongpo Xu Zhiping Wang Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks Discrete Dynamics in Nature and Society |
| title | Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks |
| title_full | Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks |
| title_fullStr | Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks |
| title_full_unstemmed | Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks |
| title_short | Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks |
| title_sort | convergence of an online split complex gradient algorithm for complex valued neural networks |
| url | http://dx.doi.org/10.1155/2010/829692 |
| work_keys_str_mv | AT huishengzhang convergenceofanonlinesplitcomplexgradientalgorithmforcomplexvaluedneuralnetworks AT dongpoxu convergenceofanonlinesplitcomplexgradientalgorithmforcomplexvaluedneuralnetworks AT zhipingwang convergenceofanonlinesplitcomplexgradientalgorithmforcomplexvaluedneuralnetworks |