The Optimatimal Algorithm Studies Of Support Vector Machines And Classification Questions

This dissertation is mainly about learning algorithms of support vector machines, which is a new approach of data mining based on the statistical learning theory and mathematical programming. Mathematical programming is an important branch of operational research. It has been extensively applied to areas of machine learning, networks problem, game theory, economics, mechanics and it is one of the most advanced areas of operational research. In addition, classification question, one of the common questions in machines learning, is also included in the paper. In approximating mathematical mode of support vector machines and misclassification minimization, and proposing the dual theories of multi-class support vector machines, some conclusions are obtained respectively as follows:In Chapter 2, a proximal algorithm called the multiplier entroy algorithm of support vector machines is constructed, which is a method by transforming the mathematical mode of support vector machines into min-max problem and solving the min-max problem using the multiplier entroy algorithm. It has the virtues of both multiplier algorithm and entroy algorithm. Entroy algorithm can turn nonsmooth problems into smooth, and multiplier algorithm can reduce the iteration in some degree and the morbid state of Hessian can be avoided. For small sample problems, especially the pre-cancer diagnosis, the algorithm can be performed efficiently. The two numerical experiments illustrate that the multiplier entroy algorithm is effective.Chapter 3 is about an approximal algorithm for misclassification minimization , which is one of the common problems in machine learning. In this chapter a new proximal mode of misclassification minimization is proposed, where piece-wise linear function is used to approximate step function. A sequence linear algorithm is constructed for solving the new model and also it is proved to terminate by finite iteration.There are few papers studying the duality theory of multi-class support vector machines. In this chapter, the property of the solution of the prime problem and the duality theorem of the mode of multi-class support vector machines are presented. Also the strict proof of these theories are given. The results given in this chapter provide the credible theory for designing algorithm of multi-class support vector machines.