# zbMATH — the first resource for mathematics

RBF neural network based on $$q$$-Gaussian function in function approximation. (English) Zbl 1267.68200
Summary: 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.
##### MSC:
 68T05 Learning and adaptive systems in artificial intelligence 92B20 Neural networks for/in biological studies, artificial life and related topics
Full Text:
##### References:
 [1] Moody J, Darken C. Fast learning in networks of locally-tuned processing units. Neural Computation, 1989, 1(2): 281–294 · doi:10.1162/neco.1989.1.2.281 [2] Kong L X, Xiao D M, Liu Y 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] Feng Y, Wu Z F, Zhong J, Ye C X, Wu K 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 · Zbl 06183852 · doi:10.1007/s11704-010-0104-5 [4] Wan L H, Zhang S H, Liu W Y, Zang S 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] Karayiannis N B, Randolph-Gips M M. On the construction and training of reformulated radial basis function neural networks. IEEE Transactions on Neural Networks, 2003, 14(4): 835–846 · Zbl 1069.68583 · doi:10.1109/TNN.2003.813841 [6] Karayiannis N B, Xiong Y 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 · doi:10.1109/TNN.2006.877538 [7] Gholizadeh S, Salajegheh E, Torkzadeh P. 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 · doi:10.1016/j.jsv.2007.10.050 [8] De Silva C R, Ranganath S, De Silva L C. Cloud basis function neural network: A modified RBF network architecture for holistic facial expression recognition. Pattern Recognition, 2008, 41(4): 1241–1253 · Zbl 1131.68080 · doi:10.1016/j.patcog.2007.09.015 [9] Harpham C, Dawson C 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] Billings S A, Wei H L, Balikhin MA. Generalized multiscale radial basis function networks. Neural Networks, 2007, 20(10): 1081–1094 · Zbl 1254.68197 · doi:10.1016/j.neunet.2007.09.017 [11] Thistleton W, Marsh J A, Nelson K, Tasllis C. Generalized Box-Müller method for generating q-Gaussian random deviates. IEEE Transactions on Information Theory, 2007, 53(12): 4805–4810 · Zbl 1326.94037 · doi:10.1109/TIT.2007.909173 [12] Wang Y, Cai Z X. A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems. Frontiers of Computer Science in China, 2009, 3(1): 38–52 · doi:10.1007/s11704-009-0010-x [13] Shi Y H, Eberhart R. Monitoring of particle swarm optimization. Frontiers of Computer Science in China, 2009, 3(1): 31–37 · doi:10.1007/s11704-009-0008-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.