Constructive Approximation to Multivariate Function by Decay RBF Neural Network

It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parame...

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Vydáno v:	IEEE transactions on neural networks Ročník 21; číslo 9; s. 1517 - 1523
Hlavní autoři:	Hou, Muzhou, Han, Xuli
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.09.2010 Institute of Electrical and Electronics Engineers
Témata:	Algorithms Applied sciences Approximation Artificial Intelligence Artificial neural networks Computer science; control theory; systems Computer Simulation - standards Computers Connectionism. Neural networks Construction Constructive neural networks Convergence of numerical methods Data processing. List processing. Character string processing Decay decay radial basis function (RBF) neural networks Exact sciences and technology Feedforward neural networks interpolation Iterative algorithms Kernel Logic and foundations Machine learning Mathematical analysis Mathematical Computing Mathematical logic, foundations, set theory Mathematical models Mathematics Memory organisation. Data processing Multi-layer neural network Multivariate Analysis Networks Neural networks Neural Networks (Computer) Neurons Proof theory and constructive mathematics Sciences and techniques of general use Software uniformly approximation Statistical analysis Constructive mathematics decay radial basis function (RBF) neural networks uniformly approximation Continuous function Neural network Radial basis function Overtraining Constructive neural networks interpolation Model matching Approximation by function Vector support machine Proof theory Feedforward
ISSN:	1045-9227, 1941-0093, 1941-0093
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Popis
Shrnutí:	It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n + 1 hidden neurons can interpolate n + 1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 ObjectType-Feature-1
ISSN:	1045-9227 1941-0093 1941-0093
DOI:	10.1109/TNN.2010.2055888