Skip to main content
Top
Published in: Neural Computing and Applications 2/2012

01-03-2012 | Original Article

Training twin support vector regression via linear programming

Authors: Ping Zhong, Yitian Xu, Yaohong Zhao

Published in: Neural Computing and Applications | Issue 2/2012

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper improves the recently proposed twin support vector regression (TSVR) by formulating it as a pair of linear programming problems instead of quadratic programming problems. The use of 1-norm distance in the linear programming TSVR as opposed to the square of the 2-norm in the quadratic programming TSVR leads to the better generalization performance and less computational time. The effectiveness of the enhanced method is demonstrated by experimental results on artificial and benchmark datasets.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Bi J, Bennett KP (2003) A geometric approach to support vector regression. Neurocomputing 55:79–108CrossRef Bi J, Bennett KP (2003) A geometric approach to support vector regression. Neurocomputing 55:79–108CrossRef
4.
go back to reference Cherkassky V, Ma YQ (2004) Practical selection of SVM parameters and noise estimation for SVM regression. Neural Netw 17:113–126CrossRefMATH Cherkassky V, Ma YQ (2004) Practical selection of SVM parameters and noise estimation for SVM regression. Neural Netw 17:113–126CrossRefMATH
5.
go back to reference Christianini V, Shawe-Taylor J (2002) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge Christianini V, Shawe-Taylor J (2002) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge
6.
go back to reference De Boor C, Rice JR (1968) Least-squares cubic spline approximation. II: variable knots, CSD Technical Report 21, Purdue University, IN De Boor C, Rice JR (1968) Least-squares cubic spline approximation. II: variable knots, CSD Technical Report 21, Purdue University, IN
7.
go back to reference Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetMATH Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetMATH
8.
go back to reference Ghorai S, Mukherjee A, Dutta PK (2009) Nonparallel plane proximal classifier. Signal Proc 89:510–522CrossRefMATH Ghorai S, Mukherjee A, Dutta PK (2009) Nonparallel plane proximal classifier. Signal Proc 89:510–522CrossRefMATH
9.
go back to reference Ghorai S, Hossain SJ, Mukherjee A, Dutta PK (2010) Newton’s method for nonparallel plane proximal classifier with unity norm hyperplanes. Signal Proc 90:93–104CrossRefMATH Ghorai S, Hossain SJ, Mukherjee A, Dutta PK (2010) Newton’s method for nonparallel plane proximal classifier with unity norm hyperplanes. Signal Proc 90:93–104CrossRefMATH
10.
go back to reference Jayadeva, Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRef Jayadeva, Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRef
11.
go back to reference Joachims T (1999) Making large-scale SVM learning practical. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods–support vector learning. MIT Press, Cambridge, pp 169–184 Joachims T (1999) Making large-scale SVM learning practical. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods–support vector learning. MIT Press, Cambridge, pp 169–184
12.
go back to reference Jiao L, Bo L, Wang L (2007) Fast sparse approximation for least squares support vector machine. IEEE Trans Neural Netw 18(3):685–697CrossRef Jiao L, Bo L, Wang L (2007) Fast sparse approximation for least squares support vector machine. IEEE Trans Neural Netw 18(3):685–697CrossRef
13.
go back to reference Keerthi SS, Shevade SK, Bhattacharyya C, Murthy K (2001) Improvements to Platt’s SMO algorithm for SVM classifier design. Neural Comput 13(3):637–649CrossRefMATH Keerthi SS, Shevade SK, Bhattacharyya C, Murthy K (2001) Improvements to Platt’s SMO algorithm for SVM classifier design. Neural Comput 13(3):637–649CrossRefMATH
14.
go back to reference Keerthi SS, Shevade SK (2003) SMO algorithm for least squares SVM formulations. Neural Comput 15(2):487–507CrossRefMATH Keerthi SS, Shevade SK (2003) SMO algorithm for least squares SVM formulations. Neural Comput 15(2):487–507CrossRefMATH
15.
go back to reference Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recogn Lett 29:1842–1848CrossRef Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recogn Lett 29:1842–1848CrossRef
16.
go back to reference Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36:7535–7543CrossRef Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36:7535–7543CrossRef
17.
go back to reference Kruif BJ, Vries A (2004) Pruning error minimization in least squares support vector machines. IEEE Trans Neural Netw 14(3):696–702CrossRef Kruif BJ, Vries A (2004) Pruning error minimization in least squares support vector machines. IEEE Trans Neural Netw 14(3):696–702CrossRef
18.
go back to reference Lee Y-J, Hsieh W-F, Huang C-M (2005) ɛ-SSVR: a smooth support vector machine forɛ -insensitive regression. IEEE Trans Knowl Data Eng 17(5):678–685CrossRef Lee Y-J, Hsieh W-F, Huang C-M (2005) ɛ-SSVR: a smooth support vector machine forɛ -insensitive regression. IEEE Trans Knowl Data Eng 17(5):678–685CrossRef
19.
go back to reference Mangasarian OL, Wild EW (2006) Multisurface proximal support vector classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRef Mangasarian OL, Wild EW (2006) Multisurface proximal support vector classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRef
20.
go back to reference Mangasarian OL (2006) Exact 1-norm support vector machine via unconstrained convex differentiable minimization. J Mach Learn Res 7:1517–1530MathSciNetMATH Mangasarian OL (2006) Exact 1-norm support vector machine via unconstrained convex differentiable minimization. J Mach Learn Res 7:1517–1530MathSciNetMATH
21.
go back to reference Osuna E, Freund R, Girosi F (1997) An improved training algorithm for support vector machines. In: Principe J, Gile L, Morgan N, Wilson E (eds) Neural networks for signal processing VII–proceedings of the 1997 IEEE workshop. IEEE. pp 276–285 Osuna E, Freund R, Girosi F (1997) An improved training algorithm for support vector machines. In: Principe J, Gile L, Morgan N, Wilson E (eds) Neural networks for signal processing VII–proceedings of the 1997 IEEE workshop. IEEE. pp 276–285
23.
go back to reference Platt JC (1999) Fast training of support vector machines using sequential minimal optimization. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in kernel methods–support vector learning. MIT Press, Cambridge, pp 185–208 Platt JC (1999) Fast training of support vector machines using sequential minimal optimization. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in kernel methods–support vector learning. MIT Press, Cambridge, pp 185–208
24.
go back to reference Shevade SK, Keerthi SS, Bhattacharyya C, Murthy KRK (2000) Improvements to the SMO algorithm for SVM regression. IEEE Trans Neural Netw 11(5):1188–1193CrossRef Shevade SK, Keerthi SS, Bhattacharyya C, Murthy KRK (2000) Improvements to the SMO algorithm for SVM regression. IEEE Trans Neural Netw 11(5):1188–1193CrossRef
25.
26.
go back to reference Suykens JAK, Gestel T, Brabanter J, Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, SingaporeCrossRefMATH Suykens JAK, Gestel T, Brabanter J, Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, SingaporeCrossRefMATH
27.
go back to reference Vapnik VN (1995) The natural of statistical learning theory. Springer, New York Vapnik VN (1995) The natural of statistical learning theory. Springer, New York
28.
go back to reference Vapnik VN (1998) Statistical learning theory. Wiley, New York Vapnik VN (1998) Statistical learning theory. Wiley, New York
29.
go back to reference Wang W, Xu Z (2004) A heuristic training for support vector regression. Neurocomputing 61:259–275CrossRef Wang W, Xu Z (2004) A heuristic training for support vector regression. Neurocomputing 61:259–275CrossRef
30.
go back to reference Zeng XY, Chen XW (2005) SMO-based pruning methods for sparse least squares support vector machines. IEEE Trans Neural Netw 16(6):1541–1546CrossRef Zeng XY, Chen XW (2005) SMO-based pruning methods for sparse least squares support vector machines. IEEE Trans Neural Netw 16(6):1541–1546CrossRef
31.
go back to reference Zhao Y, Sun J (2009) Recursive reduced least squares support vector regression. Pattern Recogn 42:837–842CrossRefMATH Zhao Y, Sun J (2009) Recursive reduced least squares support vector regression. Pattern Recogn 42:837–842CrossRefMATH
Metadata
Title
Training twin support vector regression via linear programming
Authors
Ping Zhong
Yitian Xu
Yaohong Zhao
Publication date
01-03-2012
Publisher
Springer-Verlag
Published in
Neural Computing and Applications / Issue 2/2012
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-011-0525-6

Other articles of this Issue 2/2012

Neural Computing and Applications 2/2012 Go to the issue

Premium Partner