Research Onaugmented Lagrangian Method For Support Vector Machine

Support Vector Machine(SVM)is a kind of important machine learning method,compared with the traditional learning algorithm,the ability to promote becomes better and at the same time avoids the dimension disaster situation.The core of SVM is to use some algorithm to solve the convex quadratic programming problem which is the essence of SVM,thus improving the speed and complexity of SVM training algorithm has become a hot and difficult point,how to design an efficient learning algorithm with lower time and space complexity is necessary for SVM in theory and application.This paper analyzes the existing problems of SVM algorithm,starting with the structure and the convergence speed and the time complexity of the algorithm,and proposes a new SVM model——support vector machine(SVM)Augmented Lagrange method.Firstly,the original problem of SVM is transformed into its dual problem through Lagrange duality,and then the solution to the dual problem is obtained by the augmented Lagrange method which utilizes its sparse and incomplete Cholesky decomposition,Sherman-morson-woodbury formula,line search and other techniques,thereby greatly reducing the time and space complexity of the algorithm.The contents of the paper can be summarized as follows:Chapter 1 introduces the research background and significance of this paper,the research status of SVM at home and abroad and the main research ideas.Chapter 2 introduces the basic knowledge of statistical learning theory and SVM,the semi-smooth Newton method in optimization theory,and presents the augmented Lagrange method for cone-constrained optimization.Chapter 3 introduces the main research content of this paper——SVM augmented Lagrange method and its convergence.Chapter 4 is divided into three parts.The first part introduces the parameter optimization process of SVM based on improved bird swarm algorithm.The second part introduces some skills and algorithm process of the SVM augmented Lagrange algorithm in the process of implementation.The third part presents the numerical experiments verifying the feasibility and efficiency of the algorithm proposed in this paper.