Application Based on Radial Basis Function Neural Networks

Abstract: Artificial Nenral Networks(abbreviated as ANN) is a theoretical model of Human brain networks.It is to set up an information processing systemis through imitating brain networks' structure and power.ANN's research began in the 20th century,the 40's.In the last two decades,ANN's development is very fast.ANN were applied to various fields of science,including math,engineering,computers, physics,biology,economics,management and so on.In this paper,we mainly obtained the following results based on the nature of ANN's non-linear approximation and using MATLAB's neural network toolbox.Firstly,we realized the establishment,learning,and training of BP network (abbreviated as BPNN) and Radial Basis Function(Radial Basis Fnnction) neural network(abbreviated as RBFNN).ANN's nonlinear approximation ability be reflected with simulation example.The RBFNN has simple structure,training speed and relatively strong anti-interference ability through comparative studies of BPNN and RBFNN.It also shows that RBFNN for function approximation can achieve good results.The function approximation ability of RBFNN is superior to BPNN's in many aspects.Secondly,RBFNN as a new regression method is applied to multiple linear regression models and multivariate nonlinear regression model based on the above theory.As a result,RBFNN method abtains good fitted effect and forecasted effect and it is simple and convenient in regression analysis. Finally,we forecast China's stock market prices using RBFNN.Through the 540 trading days of data of Chinese Shanghai Composite Index for the experiment to predict,we get a good prediction effect.In this paper,the Chapters as follows:Chapter 1,Preface,mainly includes the study background and the main work of this paper. Chapter 2,AAN's basic theory.Mainly includes ANN's overview,brief introduction of BPNN and RBFNN and some function approximation theorem of ANN.Main purpose is to provide a theoretical foundation for studying the ANN's function approximation ability.Chapter 3,function approximation simulation with BPNN and RBFNN.Mainly includes the design and simulation of BPNN and RBFNN using MATLAB's neural network toolbox.Chapter 4,RBFNN Model and multivariate regression model.Mainly includes RBFNN method is used to solve multiple linear regression and multivariate nonlinear regression problem.Moreover,we compare the traditional regression method with the RBFNN methods through practical applications.Chapter 5,RBFNN models for forecasting stock prices.ANN can be seen as "black box" with self-learning power,it has a very great superiority on the problem of no precise model.Because stock prices are non-linear time series,we proffer prediction model of stock price based on RBFNN in this paper,and apply the model to predict the Chinese Shanghai Composite Index.Conclusion.Mainly includes the main conclusions and shortcomings of this paper, and to make recommendations for future research.The third,fourth,fifth chapters are the core of the study…
Key words: neural networks ; function approximation ; linear regression ; nonlinear regression; stock price forecasting

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