Discussion On The Relation Of Two Types Common Classification In SVM

In recent years, Support Vector Machines (SVM) has become increasingly popular techniques in machine learning. Based on the statistical learning theory and optimization theory, SVM have been a novel method and tool. SVM transforms machine learning to solve an optimization problem, and to solve a convex quadratic programming problem by the optimization theory and method constructing algorithms. In this paper we discuss and prove the relationship of the solution to the most two kinds SVM methods: C -SVC and v -SVC, taking advantage of the solution connection between optimal and dual problem and KKT condition. At the same time we present theories and conclusions that offer other SVM methods demonstrations and illuminations in theoretical and ideological view. This paper firstly introduces SVM basic principle and all kinds of SVM methods, then penetrates into them and finds the research with drawbacks, so we discuss the relationship of the solution to the most two kinds SVM methods. The main research in this dissertation is as follows: 1.Infer and prove non-rigid convex quadratic programming problems of SVM that exist non-sole solution, but the sum of all solutions'components is equal; 2. Define a new function about the operator αto solution and the parameterC in SVM's dual problem, prove it a permanent positive and continual function, but it isn't increasing by degrees. 3.Demonstrate the solution to v -SVC existence. 4. In order to prove our theories, induct and testify solution sets homology to SVM two methods'sufficient condition lemma, the dual problem solution set existence to v -SVC must satisfy sufficient and necessary condition, as well as the solution sets homology existent and sole conclusion. Up to now, most studies are centered on the statistical learning theory and some applications. The research on SVM from the optimization point of view is also at the beginning in the world, which makes SVM run short of universal resulting in much inconvenient to hard confirming parameters. Therefore, our study is very important on the theoretical and practical aspects of SVM.