RBF neural network based on q-Gaussian function in function approximation

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

References

[1] MoodyJ, DarkenC. Fast learning in networks of locally-tuned processing units.Neural Computation, 1989, 1(2): 281–294

[2] KongL X, XiaoD M, LiuY L. Rough set and radial basis function neural network based insulation data mining fault diagnosis for power transformer.Journal of Harbin Institute of Technology (New Series), 2007, 14(2): 263–268

[3] FengY, WuZ F, ZhongJ, YeC X, WuK Q. An enhanced swarm intelligence clustering-based RBFNN classifier and its application in deep sources classification.Frontiers of Computer Science in China, 2010, 4(4): 560–570

[4] WanL H, ZhangS H, LiuW Y, ZangS Y. ARBF classification method of remote sensing image based on genetic algorithm.Journal of Harbin Institute of Technology (New Series), 2006, 13(6): 711–714

[5] KarayiannisN B, Randolph-GipsM M. On the construction and training of reformulated radial basis function neural networks.IEEE Transactions on Neural Networks, 2003, 14(4): 835–846

[6] KarayiannisN B, XiongY H. Training Reformulated radial basis function neural networks capable of identifying uncertainty in data classification.IEEE Transactions on Neural Networks, 2006, 17(5): 1222–1234

[7] GholizadehS, SalajeghehE, TorkzadehP. Structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network.Journal of Sound and Vibration, 2008, 312(1-2): 316–331

[8] De SilvaC R, RanganathS, De SilvaL C. Cloud basis function neural network: A modified RBF network architecture for holistic facial expression recognition.Pattern Recognition, 2008, 41(4): 1241–1253

[9] HarphamC, DawsonC W. The effect of different basis functions on a radial basis function network for time series prediction: A comparative study.Neurocomputing, 2006, 29(16-18): 161–170

[10] BillingsS A, WeiH L, BalikhinM A. Generalized multiscale radial basis function networks.Neural Networks, 2007, 20(10): 1081–1094

[11] ThistletonW, MarshJ A, NelsonK, TasllisC. Generalized Box-Müller method for generating q-Gaussian random deviates.IEEE Transactions on Information Theory, 2007, 53(12): 4805–4810

[12] WangY, CaiZ X. A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems.Frontiers of Computer Science in China, 2009, 3(1): 38–52

[13] ShiY H, EberhartR. Monitoring of particle swarm optimization.Frontiers of Computer Science in China, 2009, 3(1): 31–37

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg