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

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.

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.

Adaptive Genetic Algorithm for Multilayer RBF Network and its Application on Real Function Approximation

2013 ◽  
Vol 380-384 ◽  
pp. 1166-1169 ◽  
Author(s):  
Yan Hui Wang ◽  
Kun Zhang
Keyword(s):  
Genetic Algorithm ◽  
Computer Simulation ◽  
Real Function ◽  
Function Approximation ◽  
Clustering Algorithm ◽  
Least Squares Method ◽  
Adaptive Genetic Algorithm ◽  
Rbf Networks ◽  
Rbf Network ◽  
Hidden Layer

With the application of adaptive genetic algorithm to the training of multi-layer RBF networks and the optimization of the hidden layer centers and width values and using regularized least squares method, weight vectors is obtained. Computer simulation shows that the precision of real function approximation by this algorithm is much higher than the precision by clustering algorithm for multi-layer RBF networks.

Sequential function approximation with noisy data

2018 ◽  
Vol 371 ◽  
pp. 363-381 ◽  
Author(s):  
Yeonjong Shin ◽  
Kailiang Wu ◽  
Dongbin Xiu
Keyword(s):  
Function Approximation ◽  
Noisy Data ◽  
Sequential Function Approximation

Noisy Data: Incorporating Variability into Your Analysis

2014 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Richard Schwartz
Keyword(s):  
Noisy Data
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