Generalized multiscale radial basis function networks

Authors:
Stephen A. Billings;Hua-Liang Wei;Michael A. Balikhin
Affiliations:
Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK;Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK;Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK
Venue:
Neural Networks
Year:
2007

Citing 27
Cited 15

Layered neural networks with Gaussian hidden units as universal approximations

Neural Computation
Algorithms for better representation and faster learning in radial basis function networks

Advances in neural information processing systems 2
Universal approximation using radial-basis-function networks

Neural Computation
Ten lectures on wavelets

Ten lectures on wavelets
Original Contribution: On the training of radial basis function classifiers

Neural Networks
Approximation and radial-basis-function networks

Neural Computation
An introduction to wavelets

An introduction to wavelets
Recurrent radial basis function networks for adaptive noise cancellation

Neural Networks
Radial basis function network configuration using genetic algorithms

Neural Networks
An efficient method to construct a radial basis function neural network classifier

Neural Networks
Three learning phases for radial-basis-function networks

Neural Networks
A new EM-based training algorithm for RBF networks

Neural Networks
On the Kernel Widths in Radial-Basis Function Networks

Neural Processing Letters
Neural Networks: A Comprehensive Foundation (3rd Edition)

Neural Networks: A Comprehensive Foundation (3rd Edition)
Predicting the future: Advantages of semilocal units

Neural Computation
Fast learning in networks of locally-tuned processing units

Neural Computation
Regularization in the selection of radial basis function centers

Neural Computation
Variable neural networks for adaptive control of nonlinear systems

IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Sparse modeling using orthogonal forward regression with PRESS statistic and regularization

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Cooperative-competitive genetic evolution of radial basis function centers and widths for time series prediction

IEEE Transactions on Neural Networks
A hybrid linear/nonlinear training algorithm for feedforward neural networks

IEEE Transactions on Neural Networks
Reformulated radial basis neural networks trained by gradient descent

IEEE Transactions on Neural Networks
Orthogonal least squares learning algorithm for radial basis function networks

IEEE Transactions on Neural Networks
Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation

IEEE Transactions on Neural Networks
A generalized growing and pruning RBF (GGAP-RBF) neural network for function approximation

IEEE Transactions on Neural Networks
Gaussian networks for direct adaptive control

IEEE Transactions on Neural Networks
Optimal adaptive k-means algorithm with dynamic adjustment of learning rate

IEEE Transactions on Neural Networks

Rough Set Combine BP Neural Network in Next Day Load Curve Forcasting

ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks, Part II
Feature selection using tabu search with long-term memories and probabilistic neural networks

Pattern Recognition Letters
A study on the use of imputation methods for experimentation with Radial Basis Function Network classifiers handling missing attribute values: The good synergy between RBFNs and EventCovering method

Neural Networks
Clustered-Hybrid Multilayer Perceptron network for pattern recognition application

Applied Soft Computing
Sparse RBF Networks with Multi-kernels

Neural Processing Letters
Hybrid optimization scheme for radial basis function neural network

SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
Global models for patient-ventilator interactions in noninvasive ventilation with asynchronies

Computers in Biology and Medicine
Neural networks letter: Evolutionary q-Gaussian radial basis function neural networks for multiclassification

Neural Networks
Parameter estimation of q-Gaussian Radial Basis Functions Neural Networks with a Hybrid Algorithm for binary classification

Neurocomputing
RBF neural network based on q-Gaussian function in function approximation

Frontiers of Computer Science in China
Prediction of surface roughness in end milling process using intelligent systems: a comparative study

Applied Computational Intelligence and Soft Computing
Novel weighting in single hidden layer feedforward neural networks for data classification

Computers & Mathematics with Applications
2013 Special Issue: Autonomous learning derived from experimental modeling of physical laws

Neural Networks
A growing and pruning sequential learning algorithm of hyper basis function neural network for function approximation

Neural Networks
A linear recurrent kernel online learning algorithm with sparse updates

Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

A novel modelling framework is proposed for constructing parsimonious and flexible multiscale radial basis function networks (RBF). Unlike a conventional standard single scale RBF network, where all the basis functions have a common kernel width, the new network structure adopts multiscale Gaussian functions as the bases, where each selected centre has multiple kernel widths, to provide more flexible representations with better generalization properties for general nonlinear dynamical systems. As a direct extension of the traditional single scale Gaussian networks, the new multiscale network is easy to implement and is quick to learn using standard learning algorithms. A k-means clustering algorithm and an improved orthogonal least squares (OLS) algorithm are used to determine the unknown parameters in the network model including the centres and widths of the basis functions, and the weights between the basis functions. It is demonstrated that the new network can lead to a parsimonious model with much better generalization property compared with the traditional single width RBF networks.