Rotated hyperbola model for smooth support vector machine for classification  

作　　者：Wang En 

机构地区：[1]School of Social and Humanities,Xi'an Jiaotong University

出　　处：《The Journal of China Universities of Posts and Telecommunications》2018年第4期48-55,共8页中国邮电高校学报（英文版）

基　　金：supported by the National Nature Science Foundation of China under Grant ( 61100165, 61100231, 61472307 );Natural Science Foundation of Shaanxi Province ( 2016JM6004)

摘　　要：This article puts forward a novel smooth rotated hyperbola model for support vector machine( RHSSVM) for classification. As is well known,the support vector machine( SVM) is based on statistical learning theory( SLT)and performs its high precision on data classification. However,the objective function is non-differentiable at the zero point. Therefore the fast algorithms cannot be used to train and test the SVM. To deal with it,the proposed method is based on the approximation property of the hyperbola to its asymptotic lines. Firstly,we describe the development of RHSSVM from the basic linear SVM optimization programming. Then we extend the linear model to non-linear model. We prove the solution of RHSSVM is convergent,unique,and global optimal. We show how RHSSVM can be practically implemented. At last,the theoretical analysis illustrates that compared with other three typical models,the rotated hyperbola model has the least error on approximating the plus function. Meanwhile,computer simulations show that the RHSSVM can reduce the consuming time at most 54. 6% and can efficiently handle large scale and high dimensional programming.This article puts forward a novel smooth rotated hyperbola model for support vector machine( RHSSVM) for classification. As is well known,the support vector machine( SVM) is based on statistical learning theory( SLT)and performs its high precision on data classification. However,the objective function is non-differentiable at the zero point. Therefore the fast algorithms cannot be used to train and test the SVM. To deal with it,the proposed method is based on the approximation property of the hyperbola to its asymptotic lines. Firstly,we describe the development of RHSSVM from the basic linear SVM optimization programming. Then we extend the linear model to non-linear model. We prove the solution of RHSSVM is convergent,unique,and global optimal. We show how RHSSVM can be practically implemented. At last,the theoretical analysis illustrates that compared with other three typical models,the rotated hyperbola model has the least error on approximating the plus function. Meanwhile,computer simulations show that the RHSSVM can reduce the consuming time at most 54. 6% and can efficiently handle large scale and high dimensional programming.

关 键 词：CLASSIFICATION smooth technology rotated hyperbola function SVM 

分 类 号：TN[电子电信]