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

01.03.2012 | Original Article

Training twin support vector regression via linear programming

verfasst von: Ping Zhong, Yitian Xu, Yaohong Zhao

Erschienen in: Neural Computing and Applications | Ausgabe 2/2012

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat Suykens JAK, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Proc Lett 9(3):293–300MathSciNetCrossRef Suykens JAK, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Proc Lett 9(3):293–300MathSciNetCrossRef
26.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat Vapnik VN (1998) Statistical learning theory. Wiley, New York Vapnik VN (1998) Statistical learning theory. Wiley, New York
29.
Zurück zum Zitat 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.
Zurück zum Zitat 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.
Zurück zum Zitat 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
Metadaten
Titel
Training twin support vector regression via linear programming
verfasst von
Ping Zhong
Yitian Xu
Yaohong Zhao
Publikationsdatum
01.03.2012
Verlag
Springer-Verlag
Erschienen in
Neural Computing and Applications / Ausgabe 2/2012
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-011-0525-6

Weitere Artikel der Ausgabe 2/2012

Neural Computing and Applications 2/2012 Zur Ausgabe