Abstract
In this paper, we propose a novel adaptive kernel for the radial basis function neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels using the gradient descent method, thereby alleviating the need for predetermined weights. The proposed method is shown to outperform the manual fusion of the kernels on three major problems of estimation, namely nonlinear system identification, patter classification and function approximation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
W. Aftab, M. Moinuddin, M.S. Shaikh, A novel kernel for RBF based neural networks, in Abstract and Applied Analysis 2014 (2014). doi:10.1155/2014/176253
S.H.A. Ali, K. Fukase, S. Ozawa, A fast online learning algorithm of radial basis function network with locality sensitive hashing. Evol. Syst. 2016, 1–14 (2016)
G.S. Babu, S. Suresh, Meta-cognitive RBF network and its projection based learning algorithm for classification problems. Appl. Soft Comput. 13(1), 654–666 (2013)
M. Barakat, D. Lefebvre, M. Khalil, F. Druaux, O. Mustapha, Parameter selection algorithm with self adaptive growing neural network classifier for diagnosis issues. Int. J. Mach. Learn. Cybern. 4(3), 217–233 (2013)
S. Chen, C.F. Cowan, P.M. Grant, Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans. Neural Netw. 2(2), 302–309 (1991)
W. Chen, Z.J. Fu, C.S. Chen, Recent Advances in Radial Basis Function Collocation Methods (Springer, Heidelberg, 2014)
D.P.F. Cruz, R.D. Maia, L.A. da Silva, L.N. de Castro, BeeRBF: a bee-inspired data clustering approach to design RBF neural network classifiers. Neurocomputing 172, 427–437 (2016)
V. Elanayar, Y.C. Shin et al., Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans. Neural Netw. 5(4), 594–603 (1994)
M.J. Er, S. Wu, J. Lu, H.L. Toh, Face recognition with radial basis function (RBF) neural networks. IEEE Trans. Neural Netw. 13(3), 697–710 (2002)
L. Fu, M. Zhang, H. Li, Sparse RBF networks with multi-kernels. Neural Process. Lett. 32(3), 235–247 (2010)
T.R. Golub, D.K. Slonim, P. Tamayo, C. Huard, M. Gaasenbeek, J.P. Mesirov, H. Coller, M.L. Loh, J.R. Downing, M.A. Caligiuri et al., Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286(5439), 531–537 (1999)
M.A. Halali, V. Azari, M. Arabloo, A.H. Mohammadi, A. Bahadori, Application of a radial basis function neural network to estimate pressure gradient in water–oil pipelines. J. Taiwan Inst. Chem. Eng. 58, 189–202 (2016)
H.G. Han, J.F. Qiao, Adaptive computation algorithm for RBF neural network. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 342–347 (2012)
S.O. Haykin, Neural Networks: A Comprehensive Foundation (Prentice Hall PTR, Upper Saddle River, NJ, 1994)
M.M. Li, B. Verma, Nonlinear curve fitting to stopping power data using RBF neural networks. Expert Syst. Appl. 45, 161–171 (2016)
R.P. Lippmann, Pattern classification using neural networks. IEEE Commun. Mag. 27(11), 47–50 (1989)
K.S. Narendra, K. Parthasarathy, Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw. 1(1), 4–27 (1990)
A.D. Niros, G.E. Tsekouras, A novel training algorithm for RBF neural network using a hybrid fuzzy clustering approach. Fuzzy Sets Syst. 193, 62–84 (2012)
S.K. Oh, W.D. Kim, W. Pedrycz, Design of radial basis function neural network classifier realized with the aid of data preprocessing techniques: design and analysis. Int. J. Gen. Syst. 45(4), 434–454 (2016)
N.R. Pal, D. Chakraborty, Mountain and subtractive clustering method: improvements and generalizations. Int. J. Intell. Syst. 15(4), 329–341 (2000)
H. Peng, F. Long, C. Ding, Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1226–1238 (2005)
D. Psaltis, A. Sideris, A. Yamamura et al., A multilayered neural network controller. IEEE Control Syst. Mag. 8(2), 17–21 (1988)
P.D. Reiner, Algorithms for Optimal Construction and Training of Radial Basis Function Neural Networks, PhD thesis (Auburn University, 2015)
A. Tatar, S. Naseri, N. Sirach, M. Lee, A. Bahadori, Prediction of reservoir brine properties using radial basis function (RBF) neural network. Petroleum 1(4), 349–357 (2015)
D. Wettschereck, T. Dietterich, Improving the performance of radial basis function networks by learning center locations, in Advances in Neural Information Processing Systems, vol. 4 ed. by J. E. Moody, S. J. Hanson and R. P. Lippmann (Morgan Kaufmann, San Mateo, CA, 1992), pp. 1133–1140
J. Wu, J. Long, M. Liu, Evolving RBF neural networks for rainfall prediction using hybrid particle swarm optimization and genetic algorithm. Neurocomputing 148, 136–142 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Khan, S., Naseem, I., Togneri, R. et al. A Novel Adaptive Kernel for the RBF Neural Networks. Circuits Syst Signal Process 36, 1639–1653 (2017). https://doi.org/10.1007/s00034-016-0375-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-016-0375-7