Some Research For Neural Networks And Support Vector Machines

In this paper, we study some problems in neural networks and support vector machines.The theory of neural networks comes from American psychologist McCulloch and mathematician Pitts's article in 1943. They described neural network with logistic and mathematical language. Up to the end of last century, Grossberg, Hopfield and Sejnowski constitute some kinds of neural network models. These stimulated the research for the theory and application of neural networks.Since the seminal works of Hopfield and Tank [50] [51] [110], peoples started researching Hopfield neural networks' kinetic character, such as stability, convergence and so on. Neural network approach to optimization, signal processing and pattern recognition has been investigated extensively. In ths paper, we study mathematical quality of Hopfield neural networks and the application of neural networks in the fields of optimization.Support vector machines (SVM) is a new kinds of intelligent machine which advanced by the study group of Vladimir N. Vapnik in the middle of the 1990'th. SVM was based on statistical learning theory which developed in the 1970'th. It embodyed the idea and method of structure risk minimization (SRM) theory. Because of the successful application in the fields of pattern recognition, regression estimation, function approaching, risk budget, finance series analysis, density estimation and so on, SVM became the research hotshot in many study fields.In this paper, we offered some fast calculational method through separation and selection in the feature space. Moreover, we construct neural netwrok method for the quadratic programming in the training of SVM.Chapter 1, Introduction, we introduce the development history and background of neural networks and support vector machines. Moreover, we list the main results in this paper.Chapter 2, Neural network method for constrained optimization problems. For constrained optimization problems, it's hard to construct simple and effective neural network models. Recently, [66] [64] and [65] offer a sort of neural network model based on projective...