Two smooth support vector machines for ε -insensitive regression

Weizhe Gu, Wei Po Chen, Chun Hsu Ko, Yuh Jye Lee, Jein-Shan Chen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we propose two new smooth support vector machines for ε-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to ε-support vector regression (ε-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.

Original languageEnglish
Pages (from-to)171-199
Number of pages29
JournalComputational Optimization and Applications
Volume70
Issue number1
DOIs
Publication statusPublished - 2018 May 1

Fingerprint

Support vector machines
Support Vector Machine
Regression
Smoothing Function
Newton-Raphson method
Smoothing Newton Method
Support Vector Regression
Numerical Comparisons

Keywords

  • Smoothing Newton algorithm
  • Support vector machine
  • ε-insensitive loss
  • ε-smooth support vector regression

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

Two smooth support vector machines for ε -insensitive regression. / Gu, Weizhe; Chen, Wei Po; Ko, Chun Hsu; Lee, Yuh Jye; Chen, Jein-Shan.

In: Computational Optimization and Applications, Vol. 70, No. 1, 01.05.2018, p. 171-199.

Research output: Contribution to journalArticle

Gu, Weizhe ; Chen, Wei Po ; Ko, Chun Hsu ; Lee, Yuh Jye ; Chen, Jein-Shan. / Two smooth support vector machines for ε -insensitive regression. In: Computational Optimization and Applications. 2018 ; Vol. 70, No. 1. pp. 171-199.
@article{32365e8c3e024dd2b3180d214d7d38b8,
title = "Two smooth support vector machines for ε -insensitive regression",
abstract = "In this paper, we propose two new smooth support vector machines for ε-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to ε-support vector regression (ε-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.",
keywords = "Smoothing Newton algorithm, Support vector machine, ε-insensitive loss, ε-smooth support vector regression",
author = "Weizhe Gu and Chen, {Wei Po} and Ko, {Chun Hsu} and Lee, {Yuh Jye} and Jein-Shan Chen",
year = "2018",
month = "5",
day = "1",
doi = "10.1007/s10589-017-9975-9",
language = "English",
volume = "70",
pages = "171--199",
journal = "Computational Optimization and Applications",
issn = "0926-6003",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - Two smooth support vector machines for ε -insensitive regression

AU - Gu, Weizhe

AU - Chen, Wei Po

AU - Ko, Chun Hsu

AU - Lee, Yuh Jye

AU - Chen, Jein-Shan

PY - 2018/5/1

Y1 - 2018/5/1

N2 - In this paper, we propose two new smooth support vector machines for ε-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to ε-support vector regression (ε-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.

AB - In this paper, we propose two new smooth support vector machines for ε-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to ε-support vector regression (ε-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.

KW - Smoothing Newton algorithm

KW - Support vector machine

KW - ε-insensitive loss

KW - ε-smooth support vector regression

UR - http://www.scopus.com/inward/record.url?scp=85038392089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038392089&partnerID=8YFLogxK

U2 - 10.1007/s10589-017-9975-9

DO - 10.1007/s10589-017-9975-9

M3 - Article

VL - 70

SP - 171

EP - 199

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

SN - 0926-6003

IS - 1

ER -