Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks
Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The m...
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| Vydáno v: | Neural processing letters Ročník 26; číslo 3; s. 177 - 189 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Dordrecht
Springer
01.12.2007
Springer Nature B.V |
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| ISSN: | 1370-4621, 1573-773X |
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| Abstract | Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The monotonicity of the error function in the iteration is also guaranteed. |
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| AbstractList | Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The monotonicity of the error function in the iteration is also guaranteed. |
| Author | Xiong, Yan Wu, Wei Zhang, Chao |
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| Cites_doi | 10.1109/9.402231 10.1109/TNN.2005.844903 10.7551/mitpress/5236.001.0001 10.1162/neco.1989.1.1.133 10.1016/0893-6080(94)90009-4 10.1016/S0925-2312(01)00576-8 10.1016/j.neucom.2004.05.004 10.1023/A:1016249727555 10.1109/ICNNB.2005.1614626 10.1109/72.392251 |
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| Keywords | Sigma-Pi-Sigma-Pi neural networks, Batch gradient algorithm Gradient Error function 74P05 Monotonicity, 92B20 Neural network Sigma-Sigma-Pi neural networks Search algorithm Batch process Batch production Convergence, Sigma-Pi-Sigma neural networks Learning algorithm Artificial intelligence 68Q32 Algorithm analysis Monotonicity |
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| References | JY Li (9050_CR2) 1995; 23 HM Shao (9050_CR6) 2004; 2 B Lenze (9050_CR11) 1994; 7 DE Rumelhart (9050_CR1) 1986 HJ Kushner (9050_CR5) 1995; 40 B Lenze (9050_CR3) 2004; 61 DP Bertsekas (9050_CR4) 1996 W Wu (9050_CR7) 2002; 17 Y Yuan (9050_CR13) 2001 M Heywood (9050_CR12) 1995; 6 R Durbin (9050_CR10) 1989; 1 W Wu (9050_CR9) 2005; 16 9050_CR14 YC Liang (9050_CR8) 2002; 42 |
| References_xml | – volume: 40 start-page: 1403 year: 1995 ident: 9050_CR5 publication-title: IEEE Transac Automat Control doi: 10.1109/9.402231 – volume: 16 start-page: 533 year: 2005 ident: 9050_CR9 publication-title: IEEE Transac Neural Networks doi: 10.1109/TNN.2005.844903 – volume-title: Parallel distributed processing, explorations in the microstructure of cognition year: 1986 ident: 9050_CR1 doi: 10.7551/mitpress/5236.001.0001 – volume: 23 start-page: 111 year: 1995 ident: 9050_CR2 publication-title: J South China Univ Techn – volume-title: Optimization theory and methods year: 2001 ident: 9050_CR13 – volume: 1 start-page: 133 year: 1989 ident: 9050_CR10 publication-title: Neural Comput doi: 10.1162/neco.1989.1.1.133 – volume: 7 start-page: 1285 year: 1994 ident: 9050_CR11 publication-title: Neural Networks doi: 10.1016/0893-6080(94)90009-4 – volume: 42 start-page: 311 year: 2002 ident: 9050_CR8 publication-title: Neurocomputing doi: 10.1016/S0925-2312(01)00576-8 – volume: 2 start-page: 627 year: 2004 ident: 9050_CR6 publication-title: Proceed Int Symposium Comput Inform – volume: 61 start-page: 471 year: 2004 ident: 9050_CR3 publication-title: Neurocomputing doi: 10.1016/j.neucom.2004.05.004 – volume: 17 start-page: 331 year: 2002 ident: 9050_CR7 publication-title: Adv Computat Math doi: 10.1023/A:1016249727555 – volume-title: Neuro-dynamic programming year: 1996 ident: 9050_CR4 – ident: 9050_CR14 doi: 10.1109/ICNNB.2005.1614626 – volume: 6 start-page: 893 year: 1995 ident: 9050_CR12 publication-title: IEEE Transac Neural Networks doi: 10.1109/72.392251 |
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| SubjectTerms | Algorithms Applied sciences Artificial intelligence Computer science; control theory; systems Connectionism. Neural networks Convergence Error functions Exact sciences and technology Machine learning Neural networks |
| Title | Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks |
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