Strong Convergence Analysis of Batch Gradient-Based Learning Algorithm for Training Pi-Sigma Network Based on TSK Fuzzy Models
By combining of the benefits of high-order network and TSK (Tagaki-Sugeno-Kang) inference system, Pi-Sigma network is capable to dispose with the nonlinear problems much more effectively, which means it has a compacter construction, and quicker computational speed. The aim of this paper is to presen...
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| Veröffentlicht in: | Neural processing letters Jg. 43; H. 3; S. 745 - 758 |
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| Abstract | By combining of the benefits of high-order network and TSK (Tagaki-Sugeno-Kang) inference system, Pi-Sigma network is capable to dispose with the nonlinear problems much more effectively, which means it has a compacter construction, and quicker computational speed. The aim of this paper is to present a gradient-based learning method for Pi-Sigma network to train TSK fuzzy inference system. Moreover, some strong convergence results are established based on the weak convergence outcomes, which indicates that the sequence of weighted fuzzy parameters gets to a fixed point. Simulation results show the modified learning algorithm is effective to support the theoretical results. |
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| AbstractList | By combining of the benefits of high-order network and TSK (Tagaki-Sugeno-Kang) inference system, Pi-Sigma network is capable to dispose with the nonlinear problems much more effectively, which means it has a compacter construction, and quicker computational speed. The aim of this paper is to present a gradient-based learning method for Pi-Sigma network to train TSK fuzzy inference system. Moreover, some strong convergence results are established based on the weak convergence outcomes, which indicates that the sequence of weighted fuzzy parameters gets to a fixed point. Simulation results show the modified learning algorithm is effective to support the theoretical results. |
| Author | Liu, Yan Guo, Li Nan, Nan Yang, Dakun Zhang, Jianjun |
| Author_xml | – sequence: 1 givenname: Yan surname: Liu fullname: Liu, Yan email: liuyan@dlpu.edu.cn organization: School of Information Science and Engineering, Dalian Polytechnic University, School of Electronic and Information Engineering, Dalian University of Technology – sequence: 2 givenname: Dakun surname: Yang fullname: Yang, Dakun organization: School of Information Science and Technology, Sun Yat-sen University – sequence: 3 givenname: Nan surname: Nan fullname: Nan, Nan organization: Department of Electromechanical Engineering, Jining Polytechnic – sequence: 4 givenname: Li surname: Guo fullname: Guo, Li organization: School of Information Science and Engineering, Dalian Polytechnic University – sequence: 5 givenname: Jianjun surname: Zhang fullname: Zhang, Jianjun organization: School of Information Science and Engineering, Dalian Polytechnic University |
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| CitedBy_id | crossref_primary_10_1016_j_neucom_2017_06_057 crossref_primary_10_1109_ACCESS_2018_2883381 crossref_primary_10_1016_j_jfranklin_2018_06_015 crossref_primary_10_1007_s40815_020_00826_9 crossref_primary_10_1002_asjc_2400 crossref_primary_10_1049_iet_cta_2020_0090 crossref_primary_10_1088_1361_665X_aaae28 crossref_primary_10_1016_j_neucom_2017_06_061 crossref_primary_10_1007_s11063_016_9535_9 crossref_primary_10_1007_s12530_024_09606_4 |
| Cites_doi | 10.1016/j.neucom.2007.12.004 10.1016/j.fss.2012.09.015 10.1016/j.knosys.2013.01.030 10.1007/s11071-013-0880-1 10.1109/TSMCB.2007.901375 10.1109/TSMC.1985.6313399 10.1109/91.928735 10.1631/jzus.C1200008 10.1016/j.matdes.2010.02.009 10.1002/cplx.21441 10.1016/j.ins.2013.06.028 10.1109/TFUZZ.2007.905918 10.1162/neco.1992.4.3.415 10.1080/00207721.2012.670307 10.1109/21.256541 10.1016/j.ins.2009.12.030 10.1109/TNN.2002.1031939 10.1016/j.neucom.2008.12.005 10.1109/TNNLS.2012.2231436 |
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| Keywords | Pi-sigma network TSK fuzzy models Strong convergence Gradient-based learning algorithm |
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| References | Meng, Leung, Xu (CR24) 2013; 249 Mackay (CR21) 1992; 4 Shin, Ghosh (CR6) 1991; 1 Chen, Han (CR23) 2013; 18 Chen, Fei, Tian (CR3) 2013; 212 Faria, Geraldo, Vilma (CR14) 2013; 44 Charurved, Pandit, Srivastava (CR17) 2007; 8 Sun, Au, Choi (CR11) 2007; 37 Campo, Echanobe, Bosque, Tarela (CR12) 2008; 16 Liu, Yang, Yang, Wu (CR13) 2014; 34 Ampazis, Perantonis (CR20) 2002; 13 Singh, Borah (CR1) 2009; 46 Tseng, Chen, Uang (CR5) 2001; 9 Jang (CR16) 1993; 23 Jin, Jiang, Zhu (CR8) 2012; 25 Liu, Yang, Li, Wu (CR22) 2012; 13 Wu, Li, Yang, Liu (CR19) 2010; 180 Yu, Li, Luo, Su, Li (CR9) 2010; 31 Zhang, Wu, Chen, Xiong (CR10) 2008; 72 Takagi, Sugeno (CR4) 1985; 15 Lin, Chang, Lin (CR2) 2013; 24 Yuan, Sun (CR18) 2001 Ghazali, Hussain, Nawi, Mohamad (CR7) 2009; 72 Chen (CR15) 2013; 73 P Singh (9445_CR1) 2009; 46 JSR Jang (9445_CR16) 1993; 23 Y Lin (9445_CR2) 2013; 24 I Campo (9445_CR12) 2008; 16 Y Liu (9445_CR13) 2014; 34 D Meng (9445_CR24) 2013; 249 D Chen (9445_CR15) 2013; 73 P Chen (9445_CR3) 2013; 212 W Wu (9445_CR19) 2010; 180 DJC Mackay (9445_CR21) 1992; 4 T Takagi (9445_CR4) 1985; 15 W Yu (9445_CR9) 2010; 31 YX Yuan (9445_CR18) 2001 C Tseng (9445_CR5) 2001; 9 FA Faria (9445_CR14) 2013; 44 Y Shin (9445_CR6) 1991; 1 Z Sun (9445_CR11) 2007; 37 Y Jin (9445_CR8) 2012; 25 C Zhang (9445_CR10) 2008; 72 N Ampazis (9445_CR20) 2002; 13 Y Liu (9445_CR22) 2012; 13 D Chen (9445_CR23) 2013; 18 K Charurved (9445_CR17) 2007; 8 R Ghazali (9445_CR7) 2009; 72 |
| References_xml | – volume: 25 start-page: 990 issue: 6 year: 2012 end-page: 997 ident: CR8 article-title: Neural network based fuzzy identification and its application to modeling and control of complex systems publication-title: IEEE Trans Syst Man Cybern – volume: 72 start-page: 513 issue: 1–3 year: 2008 end-page: 520 ident: CR10 article-title: Convergence of BP algorithm for product unit neural networks with exponential weights publication-title: Neurocomputing doi: 10.1016/j.neucom.2007.12.004 – volume: 212 start-page: 62 year: 2013 end-page: 77 ident: CR3 article-title: Networked control for a class of T–S fuzzy systems with stochastic sensor faults publication-title: Fuzzy Sets Syst doi: 10.1016/j.fss.2012.09.015 – volume: 46 start-page: 12 year: 2009 end-page: 21 ident: CR1 article-title: High-order fuzzy-neuro expert system for time series forecasting publication-title: Knowl Based Syst doi: 10.1016/j.knosys.2013.01.030 – volume: 73 start-page: 1495 issue: 3 year: 2013 end-page: 1505 ident: CR15 article-title: Application of Takagi-Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization publication-title: Nonlinear Dyn doi: 10.1007/s11071-013-0880-1 – volume: 37 start-page: 1321 issue: 5 year: 2007 end-page: 1331 ident: CR11 article-title: A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/TSMCB.2007.901375 – volume: 15 start-page: 116 issue: 2 year: 1985 end-page: 132 ident: CR4 article-title: Fuzzy identification of systems and its applications to modeling and control publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/TSMC.1985.6313399 – volume: 9 start-page: 381 issue: 3 year: 2001 end-page: 392 ident: CR5 article-title: Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/91.928735 – year: 2001 ident: CR18 publication-title: Optimization theory and method – volume: 13 start-page: 585 issue: 8 year: 2012 end-page: 592 ident: CR22 article-title: Negative effects of sufficiently small initial weights on back-propagation neural networks publication-title: J of Zhejiang Univ Sci C (Comput & Electron) doi: 10.1631/jzus.C1200008 – volume: 31 start-page: 3282 issue: 7 year: 2010 end-page: 3288 ident: CR9 article-title: Prediction of the mechanical properties of the post-forged TiC6AlC4V alloy using fuzzy neural network publication-title: Mater Des doi: 10.1016/j.matdes.2010.02.009 – volume: 8 start-page: 1428 issue: 4 year: 2007 end-page: 1438 ident: CR17 article-title: Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch publication-title: Appl Soft Comput – volume: 18 start-page: 55 issue: 4 year: 2013 end-page: 66 ident: CR23 article-title: Prediction of multivariate chaotic time series via radial basis function neural network publication-title: Complexity doi: 10.1002/cplx.21441 – volume: 34 start-page: 114 issue: 1 year: 2014 end-page: 126 ident: CR13 article-title: A modified gradient-based neuro-fuzzy learning algorithm for pi-sigma network based on first-order takagi-sugeno system publication-title: J Math Res Appl – volume: 249 start-page: 85 issue: 10 year: 2013 end-page: 95 ident: CR24 article-title: The strong convergence of visual classification method and its applications publication-title: Inf Sci doi: 10.1016/j.ins.2013.06.028 – volume: 16 start-page: 761 issue: 3 year: 2008 end-page: 778 ident: CR12 article-title: Efficient hardware/software implementation of an adaptive neuro-fuzzy system publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2007.905918 – volume: 4 start-page: 415 issue: 3 year: 1992 end-page: 447 ident: CR21 article-title: Bayesian interpolation publication-title: Neural Comput doi: 10.1162/neco.1992.4.3.415 – volume: 44 start-page: 1956 issue: 10 year: 2013 end-page: 1969 ident: CR14 article-title: Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions publication-title: Int J Syst Sci doi: 10.1080/00207721.2012.670307 – volume: 23 start-page: 665 issue: 3 year: 1993 end-page: 685 ident: CR16 article-title: ANFIS adaptive-network-based fuzzy inference system publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/21.256541 – volume: 180 start-page: 1630 issue: 9 year: 2010 end-page: 1642 ident: CR19 article-title: A modified gradient-based neuro-fuzzy learning algorithm and its convergence publication-title: Inf Sci doi: 10.1016/j.ins.2009.12.030 – volume: 13 start-page: 1064 issue: 5 year: 2002 end-page: 1074 ident: CR20 article-title: Two highly efficient second-order algorithms for training feedforward networks publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2002.1031939 – volume: 1 start-page: 13 year: 1991 end-page: 18 ident: CR6 article-title: The Pi-Sigma networks: an efficient higher-order neural network for pattern classification and function approximation publication-title: Proc Int Joint Conf Neural Netw – volume: 72 start-page: 2359 issue: 10–12 year: 2009 end-page: 2367 ident: CR7 article-title: Non-stationary and stationary prediction of financial time series using dynamic ridge polynomial neural network publication-title: Neurocomputing doi: 10.1016/j.neucom.2008.12.005 – volume: 24 start-page: 310 issue: 2 year: 2013 end-page: 321 ident: CR2 article-title: Identification and prediction of dynamic systems using an interactively recurrent self-evolving fuzzy neural network publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2012.2231436 – volume: 212 start-page: 62 year: 2013 ident: 9445_CR3 publication-title: Fuzzy Sets Syst doi: 10.1016/j.fss.2012.09.015 – volume: 180 start-page: 1630 issue: 9 year: 2010 ident: 9445_CR19 publication-title: Inf Sci doi: 10.1016/j.ins.2009.12.030 – volume: 249 start-page: 85 issue: 10 year: 2013 ident: 9445_CR24 publication-title: Inf Sci doi: 10.1016/j.ins.2013.06.028 – volume: 72 start-page: 513 issue: 1–3 year: 2008 ident: 9445_CR10 publication-title: Neurocomputing doi: 10.1016/j.neucom.2007.12.004 – volume: 34 start-page: 114 issue: 1 year: 2014 ident: 9445_CR13 publication-title: J Math Res Appl – volume: 24 start-page: 310 issue: 2 year: 2013 ident: 9445_CR2 publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2012.2231436 – volume: 18 start-page: 55 issue: 4 year: 2013 ident: 9445_CR23 publication-title: Complexity doi: 10.1002/cplx.21441 – volume: 9 start-page: 381 issue: 3 year: 2001 ident: 9445_CR5 publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/91.928735 – volume: 73 start-page: 1495 issue: 3 year: 2013 ident: 9445_CR15 publication-title: Nonlinear Dyn doi: 10.1007/s11071-013-0880-1 – volume: 72 start-page: 2359 issue: 10–12 year: 2009 ident: 9445_CR7 publication-title: Neurocomputing doi: 10.1016/j.neucom.2008.12.005 – volume-title: Optimization theory and method year: 2001 ident: 9445_CR18 – volume: 25 start-page: 990 issue: 6 year: 2012 ident: 9445_CR8 publication-title: IEEE Trans Syst Man Cybern – volume: 15 start-page: 116 issue: 2 year: 1985 ident: 9445_CR4 publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/TSMC.1985.6313399 – volume: 8 start-page: 1428 issue: 4 year: 2007 ident: 9445_CR17 publication-title: Appl Soft Comput – volume: 31 start-page: 3282 issue: 7 year: 2010 ident: 9445_CR9 publication-title: Mater Des doi: 10.1016/j.matdes.2010.02.009 – volume: 16 start-page: 761 issue: 3 year: 2008 ident: 9445_CR12 publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2007.905918 – volume: 37 start-page: 1321 issue: 5 year: 2007 ident: 9445_CR11 publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/TSMCB.2007.901375 – volume: 4 start-page: 415 issue: 3 year: 1992 ident: 9445_CR21 publication-title: Neural Comput doi: 10.1162/neco.1992.4.3.415 – volume: 13 start-page: 1064 issue: 5 year: 2002 ident: 9445_CR20 publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2002.1031939 – volume: 13 start-page: 585 issue: 8 year: 2012 ident: 9445_CR22 publication-title: J of Zhejiang Univ Sci C (Comput & Electron) doi: 10.1631/jzus.C1200008 – volume: 1 start-page: 13 year: 1991 ident: 9445_CR6 publication-title: Proc Int Joint Conf Neural Netw – volume: 44 start-page: 1956 issue: 10 year: 2013 ident: 9445_CR14 publication-title: Int J Syst Sci doi: 10.1080/00207721.2012.670307 – volume: 23 start-page: 665 issue: 3 year: 1993 ident: 9445_CR16 publication-title: IEEE Trans Syst Man Cybern doi: 10.1109/21.256541 – volume: 46 start-page: 12 year: 2009 ident: 9445_CR1 publication-title: Knowl Based Syst doi: 10.1016/j.knosys.2013.01.030 |
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| Title | Strong Convergence Analysis of Batch Gradient-Based Learning Algorithm for Training Pi-Sigma Network Based on TSK Fuzzy Models |
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