An improved conjugate gradient algorithm for radial basis function (RBF) networks modelling

2012 ◽  
Author(s):  
Long Zhang ◽  
Kang Li ◽  
Shujuan Wang
Keyword(s):  
Radial Basis Function ◽  
Conjugate Gradient ◽  
Basis Function ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Rbf Networks ◽  
Radial Basis

Universal Approximation Using Radial-Basis-Function Networks

1991 ◽  
Vol 3 (2) ◽  
pp. 246-257 ◽  
Author(s):  
J. Park ◽  
I. W. Sandberg
Keyword(s):  
Finite Number ◽  
Radial Basis Function ◽  
Basis Function ◽  
Universal Approximation ◽  
Radial Basis Function Networks ◽  
Feedforward Networks ◽  
Rbf Networks ◽  
Smoothing Factor ◽  
Radial Basis ◽  
Hidden Layer

There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.

scholarly journals Radial basis function neural networks: a topical state-of-the-art survey

2016 ◽  
Vol 6 (1) ◽  
pp. 33-63 ◽  
Author(s):  
Ch. Sanjeev Kumar Dash ◽  
Ajit Kumar Behera ◽  
Satchidananda Dehuri ◽  
Sung-Bae Cho
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Research Work ◽  
Fine Tuning ◽  
Special Focus ◽  
Global Approximation ◽  
Rbf Networks ◽  
Fast Training ◽  
Radial Basis ◽  
Emergent Behaviors

AbstractRadial basis function networks (RBFNs) have gained widespread appeal amongst researchers and have shown good performance in a variety of application domains. They have potential for hybridization and demonstrate some interesting emergent behaviors. This paper aims to offer a compendious and sensible survey on RBF networks. The advantages they offer, such as fast training and global approximation capability with local responses, are attracting many researchers to use them in diversified fields. The overall algorithmic development of RBF networks by giving special focus on their learning methods, novel kernels, and fine tuning of kernel parameters have been discussed. In addition, we have considered the recent research work on optimization of multi-criterions in RBF networks and a range of indicative application areas along with some open source RBFN tools.

ASSESSING RBF NETWORKS USING DELVE

2000 ◽  
Vol 10 (05) ◽  
pp. 397-415 ◽  
Author(s):  
MARK ORR ◽  
JOHN HALLAM ◽  
ALAN MURRAY ◽  
TOM LEONARD
Keyword(s):  
Machine Learning ◽  
Radial Basis Function ◽  
Basis Function ◽  
The Other ◽  
Rbf Networks ◽  
Radial Basis ◽  
Regression Problems ◽  
Using Data

In this paper, different methods for training radial basis function (RBF) networks for regression problems are described and illustrated. Then, using data from the DELVE archive, they are empirically compared with each other and with some other well known methods for machine learning. Each of the RBF methods performs well on at least one DELVE task, but none are as consistent as the best of the other non-RBF methods.

RADIAL BASIS FUNCTION NETWORKS AS CHAOTIC GENERATORS FOR SECURE COMMUNICATION SYSTEMS

1999 ◽  
Vol 09 (01) ◽  
pp. 221-232 ◽  
Author(s):  
S. PAPADIMITRIOU ◽  
A. BEZERIANOS ◽  
T. BOUNTIS
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Training Data ◽  
Radial Basis Function Networks ◽  
Rbf Networks ◽  
Radial Basis

This paper improves upon a new class of discrete chaotic systems (i.e. chaotic maps) recently introduced for effective information encryption. The nonlinearity and adaptability of these systems are achieved by designing proper radial basis function networks. The potential for automatic synchronization, the lack of periodicity and the extremely large parameter spaces of these chaotic maps offer robust transmission security. The Radial Basis Function (RBF) networks offer a large number of parameters (i.e. the centers and spreads of the RBF kernels and the weights of the linear layer) while at the same time as universal approximators they have the flexibility to implement any function. The RBF networks can learn the dynamics of chaotic systems (maps or flows) and mimic them accurately by using many more parameters than the original dynamical recurrence. Since the parameter space size increases exponentially with respect to the number of parameters, the RBF based systems greatly outperform previous designs in terms of encryption security. Moreover, the learning of the dynamics from data generated by chaotic systems guarantees the chaoticity of the dynamics of the RBF networks and offers a convenient method of implementing any desirable chaotic dynamics. Since each sequence of training data gives rise to a distinct RBF configuration, theoretically there exists an infinity of possible configurations.

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