Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation

2003 ◽  
Vol 14 (6) ◽  
pp. 1478-1495 ◽  
Author(s):  
J. Gonzalez ◽  
I. Rojas ◽  
J. Ortega ◽  
H. Pomares ◽  
J. Fernandez ◽  
...  
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Approximation ◽  
Evolutionary Optimization ◽  
Radial Basis Function Networks ◽  
Radial Basis

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

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Yunfeng Wu ◽  
Xin Luo ◽  
Fang Zheng ◽  
Shanshan Yang ◽  
Suxian Cai ◽  
...  
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Approximation ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Radial Basis Function Networks ◽  
Data Sets ◽  
Radial Basis ◽  
Synthetic Function ◽  
Adaptively Adjusting

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.

SIDE EFFECTS OF NORMALISING RADIAL BASIS FUNCTION NETWORKS

1996 ◽  
Vol 07 (02) ◽  
pp. 167-179 ◽  
Author(s):  
ROBERT SHORTEN ◽  
RODERICK MURRAY-SMITH
Keyword(s):  
Side Effects ◽  
Radial Basis Function ◽  
Basis Function ◽  
Function Approximation ◽  
Partition Of Unity ◽  
Basis Functions ◽  
Radial Basis Function Networks ◽  
Rbf Network ◽  
Linear Function Approximation ◽  
Radial Basis

Normalisation of the basis function activations in a Radial Basis Function (RBF) network is a common way of achieving the partition of unity often desired for modelling applications. It results in the basis functions covering the whole of the input space to the same degree. However, normalisation of the basis functions can lead to other effects which are sometimes less desirable for modelling applications. This paper describes some side effects of normalisation which fundamentally alter properties of the basis functions, e.g. the shape is no longer uniform, maxima of basis functions can be shifted from their centres, and the basis functions are no longer guaranteed to decrease monotonically as distance from their centre increases—in many cases basis functions can ‘reactivate’, i.e. re-appear far from the basis function centre. This paper examines how these phenomena occur, discusses their relevance for non-linear function approximation and examines the effect of normalisation on the network condition number and weights.

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