Based On The Gaussian Rbf Neural Network Function Approximation And Applications

Artificial neural network has been considered to be the most challenging areas of modern artificial intelligence research focus. The theories and methods of neural network have applied in many areas, such as optimization, intelligent control and pattern recognition, etc. But many problems in these fields can be converted into the problems of approximating multivariate functions by neural network. Based on the nonlinear approximate ability of radial basis function (RBF) neural network, we investigate a RBF neural network with Gaussian activation function (referred to as Gaussian-RBF neural network) about its ability of approximating integral function and continuous function. The works of this paper are as follows:Firstly, we have founded a Gaussian-RBF neural network with n+1 single hidden layer neurons can accurately interpolate n+1 samples; then the inner and outer weights of theses Gaussian-RBF neural networks are constructed according to the samples, we give a proof that they can approximately interpolate with arbitrary precision. Further, we prove they can uniformly approximate any continuous function of any closed interval with arbitrary precision, without training.Secondly, by using Matlab neural network toolbox, we have designed one-dimensional and two-dimensional function approximation test with Gaussian-RBF neural network and BP neural network, and to both the approximation properties, generalization ability, the convergence rate, the error and other aspects of the comparison, the results show that the Gaussian-RBF neural network not only design comfortably and have a faster training speed, but also can achieve better approximation results.Finally, we constructed a model based on Gaussian-RBF neural network and forecast China's stock price using the model. And through the 300 trading days of data of the Shanghai Composite Index for the experiment to train and predict, we found that Gaussian-RBF neural network stock prediction model than the BP neural network prediction model can get a relatively better prediction effect. Theoretical analysis and experiment result show that the method of stock prediction using Gaussian-RBF neural network is feasible and efficient. It has favorable applicable foreground.