Research On Support Vector Machine Algorithm For Binary Classification Problem

Support vector machine is a tool to solve machine learning problems through optimization methods.It was first proposed by Vapnik et al.in the 1990 s.It has excellent learning ability,especially generalization ability.In recent years,data mining and machine learning have developed rapidly.Support vector machine has become an effective mean to solve the problems of “over learning”and “dimension disaster”.Its theory and algorithm are relatively mature.It is widely used in speech recognition,face recognition,text detection and recognition,time series prediction and other fields.According to the principle of maximum margin,the traditional support vector machine obtains a decision hyperplane by solving a quadratic programming problem to achieve the purpose of classification.Since then,twin support vector machines and nonparallel support vector machines have been proposed.By solving two quadratic programming problems,the decision hyperplanes corresponding to each class of sample points are obtained.Compared with support vector machines,they have stronger adaptability and generalization.For nonlinear separable data,because the selection of kernel function affects the accuracy of classification,Dagher et al.proposed a quadratic kernel free support vector machine to avoid using kernel function with a quadratic decision function.In the era of big data,data types are diversified and the scale of data is becoming larger and larger,which puts forward higher requirements for the construction of data classification model.This paper studies the existing support vector machine models from the perspective of improving the classification accuracy and universality of the algorithm.The author establishes three new classification models: L1-parallel twin support vector machine,improved nonparallel support vector machine and quadratic kernel-free twin boundary support vector machine.The corresponding algorithms are proposed.Finally,a series of numerical experiments are carried out to illustrate the effectiveness of the model.The specific content of this paper is arranged as follows:In Chapter 1,the author mainly introduces the background,significance,current situation of support vector machine and the main job of the paper.In Chapter 2,an L1-parallel twin support vector machine is proposed.On the one hand,each hyperplane is proximal to the data points of one class,on the other hand,the author considers the maximum distance from each data point to another hyperplane and increases the margin between two hyperplanes.A new optimization problem classification model is constructed and the corresponding algorithm is proposed.The results of numerical experiments show that the algorithm is effective in solving binary classification problems.In Chapter 3,an improved nonparallel support vector machine is proposed.Considering making the ?-band of each class point as small as possible,a new classification model for optimization problem is constructed.On the basis of the excellent performance of nonparallel support vector machine,an improvement makes it have better classification performance and advantages in dealing with data classification problems.The corresponding algorithm is proposed.Experimental results show that the algorithm is effective for binary classification.In Chapter 4,based on twin boundary support vector machine,a quadratic kernel-free twin boundary support vector machine is proposed.Because it is difficult to select kernel function for nonlinear separable data,a new classification model of optimization problem is constructed by introducing the idea of kernel free into double boundary support vector machine,In order to reduce the computational complexity,a quadratic kernel free double boundary least squares support vector machine,and the corresponding algorithm is proposed.The results of numerical experiments show that the algorithm is effective in dealing with classification problems.In Chapter 5,the research content of this paper is summarized,and the future research direction is put forward.