Constructive Approximation to Multivariate Function by Decay RBF Neural Network

• Published in: IEEE transactions on neural networks Vol. 21; no. 9; pp. 1517 - 1523
• Main Authors: Hou, Muzhou, Han, Xuli
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2010; Institute of Electrical and Electronics Engineers
• Subjects: 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
• DOI: 10.1109/TNN.2010.2055888

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.