A RBF Network Approach for Function Approximation

2018 ◽  
Author(s):  
Zan-Rong He ◽  
Yan-Ting Lin ◽  
Shie-Jue Lee ◽  
Chih-Hung Wu
Keyword(s):  
Function Approximation ◽  
Network Approach ◽  
Rbf Network

scholarly journals An inverse POD-RBF network approach to parameter estimation in mechanics

2012 ◽  
Vol 20 (5) ◽  
pp. 749-767 ◽  
Author(s):  
Craig A. Rogers ◽  
Alain J. Kassab ◽  
Eduardo A. Divo ◽  
Ziemowit Ostrowski ◽  
Ryszard A. Bialecki
Keyword(s):  
Parameter Estimation ◽  
Network Approach ◽  
Rbf Network

PRUNING AND MODEL-SELECTING ALGORITHMS IN THE RBF FRAMEWORKS CONSTRUCTED BY SUPPORT VECTOR LEARNING

2006 ◽  
Vol 16 (04) ◽  
pp. 283-293 ◽  
Author(s):  
PEI-YI HAO ◽  
JUNG-HSIEN CHIANG
Keyword(s):  
Function Approximation ◽  
Synthetic Data ◽  
Support Vector ◽  
Detection Problem ◽  
Data Simulation ◽  
Penalty Term ◽  
Rbf Network ◽  
Sample Classification ◽  
Pruning Algorithms ◽  
And Function

This paper presents the pruning and model-selecting algorithms to the support vector learning for sample classification and function regression. When constructing RBF network by support vector learning we occasionally obtain redundant support vectors which do not significantly affect the final classification and function approximation results. The pruning algorithms primarily based on the sensitivity measure and the penalty term. The kernel function parameters and the position of each support vector are updated in order to have minimal increase in error, and this makes the structure of SVM network more flexible. We illustrate this approach with synthetic data simulation and face detection problem in order to demonstrate the pruning effectiveness.

Function approximation from noisy data by an incremental RBF network

1999 ◽  
Vol 32 (12) ◽  
pp. 2081-2083 ◽  
Author(s):  
Menita Carozza ◽  
Salvatore Rampone
Keyword(s):  
Function Approximation ◽  
Noisy Data ◽  
Rbf Network

scholarly journals Using Radial Basis Function Networks for Function Approximation and Classification

2012 ◽  
Vol 2012 ◽  
pp. 1-34 ◽  
Author(s):  
Yue Wu ◽  
Hui Wang ◽  
Biaobiao Zhang ◽  
K.-L. Du
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Approximation ◽  
System Modeling ◽  
Rbf Network ◽  
Network Learning ◽  
Radial Basis ◽  
Comprehensive Survey ◽  
Dynamic System Modeling ◽  
Complex Valued

The radial basis function (RBF) network has its foundation in the conventional approximation theory. It has the capability of universal approximation. The RBF network is a popular alternative to the well-known multilayer perceptron (MLP), since it has a simpler structure and a much faster training process. In this paper, we give a comprehensive survey on the RBF network and its learning. Many aspects associated with the RBF network, such as network structure, universal approimation capability, radial basis functions, RBF network learning, structure optimization, normalized RBF networks, application to dynamic system modeling, and nonlinear complex-valued signal processing, are described. We also compare the features and capability of the two models.

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.

Navigating Expensive and Complex Design Spaces Using Genetic Algorithms

1999 ◽  
Author(s):  
David C. Zimmerman
Keyword(s):  
Function Approximation ◽  
Design Space ◽  
Optimization Technique ◽  
Computational Cost ◽  
Approximation Procedure ◽  
Network Approach ◽  
Neural Network Approach ◽  
Design Problems ◽  
Complex Design ◽  
Single Function

Abstract The overall objective of this study is to formulate and study a generic procedure for navigating expensive and complex design spaces. The term generic is meant to imply that the procedure would be equally valid in exploring design problems in a multitude of fields. The term expensive design space implies that the computational cost, or burden, associated with a single function is considered “large”. What is desired is a methodology which can identify “promising regions” of the design space using as few function evaluations as possible. To approach this problem, a neural network approach is developed to serve as an inexpensive and generic function approximation procedure. The genetic algorithm was selected as the optimization technique based on its ability to search multi-modal, discontinuous, mixed parameter, and noisy design spaces.

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