Skip to main content

2016 | OriginalPaper | Buchkapitel

Linear and Nonlinear Classifiers of Data with Support Vector Machines and Generalized Support Vector Machines

verfasst von : Talat Nazir, Xiaomin Qi, Sergei Silvestrov

Erschienen in: Engineering Mathematics II

Verlag: Springer International Publishing

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

search-config
loading …

Abstract

The support vector machine for linear and nonlinear classification of data is studied. The notion of generalized support vector machine for data classifications is used. The problem of generalized support vector machine is shown to be equivalent to the problem of generalized variational inequality and various results for the existence of solutions are established. Moreover, examples supporting the results are provided.

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

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!

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"

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!

Literatur
1.
Zurück zum Zitat Adankon, M.M., Cheriet, M.: Model selection for the LS-SVM. Application to handwriting recognition. Pattern Recognit. 42(12), 3264–3270 (2009)CrossRefMATH Adankon, M.M., Cheriet, M.: Model selection for the LS-SVM. Application to handwriting recognition. Pattern Recognit. 42(12), 3264–3270 (2009)CrossRefMATH
2.
Zurück zum Zitat Cortes, C., Vapnik, V.N.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)MATH Cortes, C., Vapnik, V.N.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)MATH
3.
Zurück zum Zitat Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other Kernel Based Learning Methods. Cambridge University Press, Cambridge (2000) Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other Kernel Based Learning Methods. Cambridge University Press, Cambridge (2000)
4.
Zurück zum Zitat Guyon, I., Weston, J., Barnhill, S., Vapnik, V.: Gene selection for cancer classification using support vector machines. Mach. Learn. 46(1–3), 389–422 (2002)CrossRefMATH Guyon, I., Weston, J., Barnhill, S., Vapnik, V.: Gene selection for cancer classification using support vector machines. Mach. Learn. 46(1–3), 389–422 (2002)CrossRefMATH
5.
Zurück zum Zitat Joachims, T.: Text categorization with support vector machines: learning with many relevant features. In: Proceedings of the European Conference on Machine Learning. Springer, Heidelberg (1998) Joachims, T.: Text categorization with support vector machines: learning with many relevant features. In: Proceedings of the European Conference on Machine Learning. Springer, Heidelberg (1998)
6.
Zurück zum Zitat Khan, N., Ksantini, R., Ahmad, I., Boufama, B.: A novel SVM+NDA model for classification with an application to face recognition. Pattern Recognit. 45(1), 66–79 (2012)CrossRefMATH Khan, N., Ksantini, R., Ahmad, I., Boufama, B.: A novel SVM+NDA model for classification with an application to face recognition. Pattern Recognit. 45(1), 66–79 (2012)CrossRefMATH
7.
Zurück zum Zitat Li, S., Kwok, J.T., Zhu, H., Wang, Y.: Texture classification using the support vector machines. Pattern Recognit. 36(12), 2883–2893 (2003)CrossRefMATH Li, S., Kwok, J.T., Zhu, H., Wang, Y.: Texture classification using the support vector machines. Pattern Recognit. 36(12), 2883–2893 (2003)CrossRefMATH
8.
Zurück zum Zitat Liu, R., Wang, Y., Baba, T., Masumoto, D., Nagata, S.: SVM-based active feedback in image retrieval using clustering and unlabeled data. Pattern Recognit. 41(8), 2645–2655 (2008)CrossRefMATH Liu, R., Wang, Y., Baba, T., Masumoto, D., Nagata, S.: SVM-based active feedback in image retrieval using clustering and unlabeled data. Pattern Recognit. 41(8), 2645–2655 (2008)CrossRefMATH
9.
Zurück zum Zitat Michel, P., Kaliouby, R.E.: Real time facial expresion recognition in video using support vector machines. In: Proceedings of ICMI’03, pp. 258–264 (2003) Michel, P., Kaliouby, R.E.: Real time facial expresion recognition in video using support vector machines. In: Proceedings of ICMI’03, pp. 258–264 (2003)
10.
Zurück zum Zitat Noble, W.S.: Support Vector Machine Applications in Computational Biology. MIT Press, Cambridge (2004) Noble, W.S.: Support Vector Machine Applications in Computational Biology. MIT Press, Cambridge (2004)
11.
Zurück zum Zitat Shao, Y., Lunetta, R.S.: Comparison of support vector machine, neural network, and CART algorithms for the land-cover classification using limited training data points. ISPRS J. Photogramm. Remote Sens. 70, 78–87 (2012)CrossRef Shao, Y., Lunetta, R.S.: Comparison of support vector machine, neural network, and CART algorithms for the land-cover classification using limited training data points. ISPRS J. Photogramm. Remote Sens. 70, 78–87 (2012)CrossRef
12.
Zurück zum Zitat Shao, Y.H., Chen, W.J., Deng, N.Y.: Nonparallel hyperplane support vector machine for binary classification problems. Inf. Sci. 263, 22–35 (2014)MathSciNetCrossRefMATH Shao, Y.H., Chen, W.J., Deng, N.Y.: Nonparallel hyperplane support vector machine for binary classification problems. Inf. Sci. 263, 22–35 (2014)MathSciNetCrossRefMATH
13.
Zurück zum Zitat Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1996)MATH Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1996)MATH
14.
Zurück zum Zitat Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)MATH Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)MATH
15.
Zurück zum Zitat Wang, D., Qi, X., Wen, S., Deng, M.: SVM based fault classifier design for a water level control system. In: Proceedings of 2013 International Conference on Advanced Mechatronic Systems, pp. 152–157. Luoyang, China (2013) Wang, D., Qi, X., Wen, S., Deng, M.: SVM based fault classifier design for a water level control system. In: Proceedings of 2013 International Conference on Advanced Mechatronic Systems, pp. 152–157. Luoyang, China (2013)
16.
Zurück zum Zitat Wang, D., Qi, X., Wen, S., Dan, Y., Ouyang, L., Deng, M.: Robust nonlinear control and SVM classifier based fault diagnosis for a water level process. ICIC Express Lett. 5(1), 767–774 (2014) Wang, D., Qi, X., Wen, S., Dan, Y., Ouyang, L., Deng, M.: Robust nonlinear control and SVM classifier based fault diagnosis for a water level process. ICIC Express Lett. 5(1), 767–774 (2014)
17.
Zurück zum Zitat Wang, X.Y., Wang, T., Bu, J.: Color image segmentation using pixel wise support vector machine classification. Pattern Recognit. 44(4), 777–787 (2011)CrossRefMATH Wang, X.Y., Wang, T., Bu, J.: Color image segmentation using pixel wise support vector machine classification. Pattern Recognit. 44(4), 777–787 (2011)CrossRefMATH
18.
Zurück zum Zitat Weston, J., Watkins, C.: Multi-class support vector machines. Technical report CSD-TR- 98-04, Department of Computer Science, Royal Holloway, University of London (1998) Weston, J., Watkins, C.: Multi-class support vector machines. Technical report CSD-TR- 98-04, Department of Computer Science, Royal Holloway, University of London (1998)
19.
Zurück zum Zitat Wu, Y.C., Lee, Y.-S., Yang, J.-C.: Robust and efficient multiclass SVM models for phrase pattern recognition. Pattern Recognit. 41(9), 2874–2889 (2008)CrossRefMATH Wu, Y.C., Lee, Y.-S., Yang, J.-C.: Robust and efficient multiclass SVM models for phrase pattern recognition. Pattern Recognit. 41(9), 2874–2889 (2008)CrossRefMATH
20.
Zurück zum Zitat Xue, Z., Ming, D., Song, W., Wan, B., Jin, S.: Infrared gait recognition based on wavelet transform and support vector machine. Pattern Recognit. 43(8), 2904–2910 (2010)CrossRefMATH Xue, Z., Ming, D., Song, W., Wan, B., Jin, S.: Infrared gait recognition based on wavelet transform and support vector machine. Pattern Recognit. 43(8), 2904–2910 (2010)CrossRefMATH
21.
Zurück zum Zitat Zhao, Z., Liu, J., Cox, J.: Safe and efficient screening for sparse support vector machine. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 14, pp. 542–551, New York, NY, USA (2014) Zhao, Z., Liu, J., Cox, J.: Safe and efficient screening for sparse support vector machine. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 14, pp. 542–551, New York, NY, USA (2014)
22.
Zurück zum Zitat Zuo, R., Carranza, E.J.M.: Support vector machine: a tool for mapping mineral prospectivity. Comput. Geosci. 37(12), 1967–1975 (2011)CrossRef Zuo, R., Carranza, E.J.M.: Support vector machine: a tool for mapping mineral prospectivity. Comput. Geosci. 37(12), 1967–1975 (2011)CrossRef
Metadaten
Titel
Linear and Nonlinear Classifiers of Data with Support Vector Machines and Generalized Support Vector Machines
verfasst von
Talat Nazir
Xiaomin Qi
Sergei Silvestrov
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-42105-6_18