Rotated hyperbola model for smooth support vector machine for classification

doi:10.19682/j.cnki.1005-8885.2018.1016

中国邮电高校学报(英文版) ›› 2018, Vol. 25 ›› Issue (4): 48-55.doi: 10.19682/j.cnki.1005-8885.2018.1016

• Artificial Intelligence • 上一篇下一篇

Rotated hyperbola model for smooth support vector machine for classification

Wang En

School of Social and Humanities, Xi’an Jiaotong University, Xi’an 710049, China

收稿日期:2017-12-13 修回日期:2018-08-16 出版日期:2018-08-30 发布日期:2018-11-02
通讯作者: Wang En,E-mail:welg_glew@qq.com E-mail:welg_glew@qq.com
作者简介:Wang En,E-mail:welg_glew@qq.com
基金资助:
This work was supported by the National Nature Science Foundation of China under Grant (61100165, 61100231, 61472307), Natural Science Foundation of Shaanxi Province (2016JM6004).

Rotated hyperbola model for smooth support vector machine for classification

Wang En

School of Social and Humanities, Xi’an Jiaotong University, Xi’an 710049, China

Received:2017-12-13 Revised:2018-08-16 Online:2018-08-30 Published:2018-11-02
Contact: Wang En,E-mail:welg_glew@qq.com E-mail:welg_glew@qq.com
About author:Wang En,E-mail:welg_glew@qq.com
Supported by:
This work was supported by the National Nature Science Foundation of China under Grant (61100165, 61100231, 61472307), Natural Science Foundation of Shaanxi Province (2016JM6004).

摘要/Abstract

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.

关键词: classification, smooth technology, rotated hyperbola function, SVM

Abstract: 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.

Key words: classification, smooth technology, rotated hyperbola function, SVM

Wang En. Rotated hyperbola model for smooth support vector machine for classification[J]. JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOM, 2018, 25(4): 48-55.

参考文献

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Rotated hyperbola model for smooth support vector machine for classification

Rotated hyperbola model for smooth support vector machine for classification

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