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Frontiers of Computer Science

ISSN 2095-2228

ISSN 2095-2236(Online)

CN 10-1014/TP

Postal Subscription Code 80-970

2018 Impact Factor: 1.129

Front Comput Sci Chin    2011, Vol. 5 Issue (4) : 381-386    https://doi.org/10.1007/s11704-011-1041-7
RESEARCH ARTICLE
RBF neural network based on q-Gaussian function in function approximation
Wei ZHAO(), Ye SAN
Control and Simulation Center, Harbin Institute of Technology, Harbin 150001, China
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Abstract

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.

Keywords radial basis function (RBF) neural network      q-Gaussian function      particle swarm optimization algorithm      function approximation     
Corresponding Author(s): ZHAO Wei,Email:zhaoweidaqing@yahoo.com.cn   
Issue Date: 05 December 2011
 Cite this article:   
Wei ZHAO,Ye SAN. RBF neural network based on q-Gaussian function in function approximation[J]. Front Comput Sci Chin, 2011, 5(4): 381-386.
 URL:  
https://academic.hep.com.cn/fcs/EN/10.1007/s11704-011-1041-7
https://academic.hep.com.cn/fcs/EN/Y2011/V5/I4/381
Fig.1  -Gaussian distribution
Fig.2  RBF neural network structure
FunctionHidden numberLRBFCRBFGRBFqGRBF
MSE TrainMSE TestTraining time/sMSE TrainMSE TestTraining time/sMSE TrainMSE TestTraining time/sMSE TrainMSE TestTraining time/s
f12052.24680.661012062.73674.811009458.68666.621290149.87719.0112902
3050.28663.901012068.58696.751009457.23680.841288747.87679.5412894
4062.90697.051014273.22722.441011759.61700.891284751.47726.0912934
f2200.51280.4145101020.53340.4319100910.53300.4390128910.44630.388112860
300.48270.3900101210.53900.4267100840.53690.4218129040.51290.386412855
400.48510.3872101400.52000.4241101020.52720.4307129180.51610.400712898
f3202.50672.9985100980.46160.3685100770.09760.0083128260.11010.004112836
302.85792.9257101190.69900.5297100950.08820.0070128250.10090.003712865
402.23702.2948101430.55510.5175101290.11290.0046128460.09650.011912900
f4200.41050.3085100960.39770.3047101250.41520.3020128250.38900.287812893
300.37460.3002101170.40170.3047101250.40130.3032128320.35290.290912895
400.40600.2984101440.40340.3024101420.36730.3072128440.37150.296812931
f5200.21260.1134101070.15050.0553100970.12000.0277128130.11660.021112863
300.19180.1049101240.14380.0555100890.11780.0320128170.11970.023112861
400.21380.1268101440.16910.0483101100.13200.0382129220.12030.023312899
Tab.1  Performance comparison of the four different RBF neural networks for approximating five functions
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