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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 913897, 14 pages
Research Article

Adaptive Linear and Normalized Combination of Radial Basis Function Networks for Function Approximation and Regression

1School of Information Science and Technology, Xiamen University, 422 Si Ming South Road, Xiamen, Fujian 361005, China
2School of Science and Technology, The Open University of Hong Kong, 30 Good Shepherd Street, Ho Man Tin, Kowloon, Hong Kong

Received 2 November 2013; Revised 28 February 2014; Accepted 28 February 2014; Published 30 March 2014

Academic Editor: Wei Bian

Copyright © 2014 Yunfeng Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a novel adaptive linear and normalized combination (ALNC) method that can be used to combine the component radial basis function networks (RBFNs) to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error) and the better fidelity (characterized by normalized correlation coefficient) of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.