Skip to main content
Erschienen in: Neural Computing and Applications 1/2013

01.05.2013 | Original Article

Multiple birth support vector machine for multi-class classification

verfasst von: Zhi-Xia Yang, Yuan-Hai Shao, Xiang-Sun Zhang

Erschienen in: Neural Computing and Applications | Sonderheft 1/2013

Einloggen

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

search-config
loading …

Abstract

For multi-class classification problem, a novel algorithm, called as multiple birth support vector machine (MBSVM), is proposed, which can be considered as an extension of twin support vector machine. Our MBSVM has been compared with the several typical support vector machines. From theoretical point of view, it has been shown that its computational complexity is remarkably low, especially when the class number K is large. Based on our MBSVM, the dual problems of MBSVM are equivalent to symmetric mixed linear complementarity problems to which successive overrelaxation (SOR) can be directly applied. We establish our SOR algorithm for MBSVM. The SOR algorithm handles one data point at a time, so it can process large dataset that need no reside in memory. From practical point of view, its accuracy has been validated by the preliminary numerical experiments.

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!

Literatur
1.
Zurück zum Zitat Cortes C, Vapnik V (1995) Support-vector network. Mach Learn 20:273–297MATH Cortes C, Vapnik V (1995) Support-vector network. Mach Learn 20:273–297MATH
2.
Zurück zum Zitat Vapnik V (1998) The nature of statistical learning, 2nd edn. Springer, New York Vapnik V (1998) The nature of statistical learning, 2nd edn. Springer, New York
3.
Zurück zum Zitat Jayadeva R, Khemchandani R, Chandra S (2007) Twin support vector machine for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRef Jayadeva R, Khemchandani R, Chandra S (2007) Twin support vector machine for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRef
4.
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
5.
Zurück zum Zitat Balasundaram S, Kapil N (2010) Application of lagrangian twin support vector machines for classification. Second international conference on machine learning and computing, pp 193–397 Balasundaram S, Kapil N (2010) Application of lagrangian twin support vector machines for classification. Second international conference on machine learning and computing, pp 193–397
6.
Zurück zum Zitat Ghorai S, Mukherjee A, Dutta PK (2009) Nonparallel plane proximal classifier. Signal Process 89:510–522MATHCrossRef Ghorai S, Mukherjee A, Dutta PK (2009) Nonparallel plane proximal classifier. Signal Process 89:510–522MATHCrossRef
7.
8.
Zurück zum Zitat Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recognit Lett 29:1842–1848CrossRef Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recognit Lett 29:1842–1848CrossRef
9.
Zurück zum Zitat Kumar MA, Khemchandani R, Gopal M, Chandra S (2010) Knowledge based least squares twin support vector machines. Inf Sci 180:4606–4618MATHCrossRef Kumar MA, Khemchandani R, Gopal M, Chandra S (2010) Knowledge based least squares twin support vector machines. Inf Sci 180:4606–4618MATHCrossRef
10.
Zurück zum Zitat Peng XJ (2010) Least squares twin support vector hypersphere (LS-TSVH) for pattern recognition. Expert Syst Appl 37:8371–8378CrossRef Peng XJ (2010) Least squares twin support vector hypersphere (LS-TSVH) for pattern recognition. Expert Syst Appl 37:8371–8378CrossRef
11.
Zurück zum Zitat Peng XJ (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23:365–372CrossRef Peng XJ (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23:365–372CrossRef
12.
Zurück zum Zitat Peng XJ (2010) Primal twin support vector regression and its sparse approximation. Neurocomputing 73(16–18):2846–2858CrossRef Peng XJ (2010) Primal twin support vector regression and its sparse approximation. Neurocomputing 73(16–18):2846–2858CrossRef
13.
Zurück zum Zitat Peng XJ (2010) A ν-twin support vector machine (ν-TSVM) classifier and its geometric algorithms. Inf Sci 180(20):3863–3875MATHCrossRef Peng XJ (2010) A ν-twin support vector machine (ν-TSVM) classifier and its geometric algorithms. Inf Sci 180(20):3863–3875MATHCrossRef
14.
Zurück zum Zitat Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvoments on twin support vector machine. IEEE Trans Neural Netw 22(6):962–968CrossRef Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvoments on twin support vector machine. IEEE Trans Neural Netw 22(6):962–968CrossRef
15.
Zurück zum Zitat Ye QL, Zhao CX, Ye N (2010) Least squares twin support vector machine classification via maximum one-class within class variance. Optimization methods and software, 18 August Ye QL, Zhao CX, Ye N (2010) Least squares twin support vector machine classification via maximum one-class within class variance. Optimization methods and software, 18 August
16.
Zurück zum Zitat Ye QL, Zhao CX, Ye N, Zheng H, Chen XB (2010) A feature selection method for nonparallel plane support vector machine classification. Optimization methods and software, 29 November Ye QL, Zhao CX, Ye N, Zheng H, Chen XB (2010) A feature selection method for nonparallel plane support vector machine classification. Optimization methods and software, 29 November
17.
Zurück zum Zitat Ye QL, Zhao CX, Ye N, Chen XB (2011) Localized twin SVM via convex minimization. Neurocomputing 74:580–587CrossRef Ye QL, Zhao CX, Ye N, Chen XB (2011) Localized twin SVM via convex minimization. Neurocomputing 74:580–587CrossRef
18.
Zurück zum Zitat Nemmour H, Chibani Y (2006) Multi-class SVMs based on fuzzy integral mixture for handwritten digit recognition. Geometric modeling and imaging—new trends, pp 145–149 Nemmour H, Chibani Y (2006) Multi-class SVMs based on fuzzy integral mixture for handwritten digit recognition. Geometric modeling and imaging—new trends, pp 145–149
19.
Zurück zum Zitat Rogers S, Girolami M, Krebs R, Mischak H (2005) Disease classification from capillary electrophoresis: mass spectrometry. Lect Notes Comput Sci 3686:183–191CrossRef Rogers S, Girolami M, Krebs R, Mischak H (2005) Disease classification from capillary electrophoresis: mass spectrometry. Lect Notes Comput Sci 3686:183–191CrossRef
20.
Zurück zum Zitat Ding CH, Dubchak I (2001) Multi-class protein fold recognition using support vector machines and neural networks. Bioinform Biol Insights 17:349–358CrossRef Ding CH, Dubchak I (2001) Multi-class protein fold recognition using support vector machines and neural networks. Bioinform Biol Insights 17:349–358CrossRef
21.
Zurück zum Zitat Allwein EL, Schapire RE, Singer Y (2001) Reducing multiclass to binary: a unifying approach for margin classifiers. J Mach Learn Res 1:113–141MathSciNetMATH Allwein EL, Schapire RE, Singer Y (2001) Reducing multiclass to binary: a unifying approach for margin classifiers. J Mach Learn Res 1:113–141MathSciNetMATH
22.
Zurück zum Zitat Bennett KP (1999) Combining support vector and mathematical programming methods for classification. In: Scholkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods: support vector learning. MIT Press, Cambridge, MA, pp 307–326 Bennett KP (1999) Combining support vector and mathematical programming methods for classification. In: Scholkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods: support vector learning. MIT Press, Cambridge, MA, pp 307–326
23.
Zurück zum Zitat Crammer K, Singer Y (2002) On the learnability and design of output codes for multiclass problems. Mach Learn 47:201–233MATHCrossRef Crammer K, Singer Y (2002) On the learnability and design of output codes for multiclass problems. Mach Learn 47:201–233MATHCrossRef
24.
Zurück zum Zitat Dietterich TG, Bakiri G (1995) Solving multiclass learning problems via error-correcting output codes. J Artif Intell Res 2:263–286MATH Dietterich TG, Bakiri G (1995) Solving multiclass learning problems via error-correcting output codes. J Artif Intell Res 2:263–286MATH
25.
Zurück zum Zitat Hastie TJ, Ribshirani RJ (1998) Classification by pairwise coupling. In: Jordan MI, Kearns MJ, Solla SA (eds) Advances in neural information processing systems 10. MIT Press, Cambridge, MA, pp 507–513 Hastie TJ, Ribshirani RJ (1998) Classification by pairwise coupling. In: Jordan MI, Kearns MJ, Solla SA (eds) Advances in neural information processing systems 10. MIT Press, Cambridge, MA, pp 507–513
26.
Zurück zum Zitat Kreβ U (1999) Pairwise classification and support vector machines. In: Scholkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods: support vector learning. MIT Press, Cambridge, MA, pp 255–268 Kreβ U (1999) Pairwise classification and support vector machines. In: Scholkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods: support vector learning. MIT Press, Cambridge, MA, pp 255–268
27.
Zurück zum Zitat Platt JC, Cristianini N, Shawe-Taylor J (2000) Large margin DAGs for multiclass classification. Adv Neural Inf Process Syst 12:547–553 Platt JC, Cristianini N, Shawe-Taylor J (2000) Large margin DAGs for multiclass classification. Adv Neural Inf Process Syst 12:547–553
28.
Zurück zum Zitat Crammer K, Singer Y (2002) On the algorithmic implementation of multiclass kernel-based vector machines. J Mach Learn Res 2:265–292MATH Crammer K, Singer Y (2002) On the algorithmic implementation of multiclass kernel-based vector machines. J Mach Learn Res 2:265–292MATH
29.
Zurück zum Zitat Lee Y, Lin Y, Wahba G (2001) Multicategory support vector machines. Comput Sci Stat 33:498–512 Lee Y, Lin Y, Wahba G (2001) Multicategory support vector machines. Comput Sci Stat 33:498–512
30.
Zurück zum Zitat Weston J, Watkins C (1998) Multi-class support vector machines. CSD-TR-98-04 royal holloway. University of London, Egham, UK Weston J, Watkins C (1998) Multi-class support vector machines. CSD-TR-98-04 royal holloway. University of London, Egham, UK
31.
Zurück zum Zitat Mangasarian OL, Musicant DR (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Netw 10(5):1032–1037CrossRef Mangasarian OL, Musicant DR (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Netw 10(5):1032–1037CrossRef
32.
Zurück zum Zitat Bottou L, Cortes C, Denker JS, Drucher H, Guyon I, Jackel LD, LeCun Y, M\(\ddot{u}\)ller UA, Sackinger E, Simard P, Vapnik V (1994) Comparison of classifier methods: a case study in handwriting digit recognition. In: IAPR (eds) Proceedings of the international conference on pattern recognition. IEEE Computer Society Press, pp 77–82 Bottou L, Cortes C, Denker JS, Drucher H, Guyon I, Jackel LD, LeCun Y, M\(\ddot{u}\)ller UA, Sackinger E, Simard P, Vapnik V (1994) Comparison of classifier methods: a case study in handwriting digit recognition. In: IAPR (eds) Proceedings of the international conference on pattern recognition. IEEE Computer Society Press, pp 77–82
33.
Zurück zum Zitat Moreira M, Mayoraz E (1998) Improved pairwise coupling classification with correcting classifiers. In: Nédellec C, Rouveirol C (eds) Proceedings of the ECML-98. Chemnitz, Germany, pp 160–171 Moreira M, Mayoraz E (1998) Improved pairwise coupling classification with correcting classifiers. In: Nédellec C, Rouveirol C (eds) Proceedings of the ECML-98. Chemnitz, Germany, pp 160–171
34.
Zurück zum Zitat Platt JC (1999) Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In: Smola AJ, Bartlett P, Schölkopf B, Schuurmans D (eds) Advances in large margin classifiers. MIT Press, Cambridge, MA Platt JC (1999) Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In: Smola AJ, Bartlett P, Schölkopf B, Schuurmans D (eds) Advances in large margin classifiers. MIT Press, Cambridge, MA
35.
Zurück zum Zitat Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The John Hopkins University Press, Baltimore Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The John Hopkins University Press, Baltimore
36.
Zurück zum Zitat Fung G, Mangasarian OL (2001) Proximal support vector machine classifiers. In: 7th International proceedings on knowledge discovery and data mining, pp 77–86 Fung G, Mangasarian OL (2001) Proximal support vector machine classifiers. In: 7th International proceedings on knowledge discovery and data mining, pp 77–86
37.
Zurück zum Zitat Luo ZQ, Tseng P (1993) Error bounds and convergence analysis of feasible descent methods: a general approach. Ann Oper Res 46:157–178MathSciNetCrossRef Luo ZQ, Tseng P (1993) Error bounds and convergence analysis of feasible descent methods: a general approach. Ann Oper Res 46:157–178MathSciNetCrossRef
38.
Zurück zum Zitat Hsu CW, Lin CJ (2002) A comparison of methods for multiclass support vector machines. IEEE Trans Neural Netw 13(2):415–425CrossRef Hsu CW, Lin CJ (2002) A comparison of methods for multiclass support vector machines. IEEE Trans Neural Netw 13(2):415–425CrossRef
Metadaten
Titel
Multiple birth support vector machine for multi-class classification
verfasst von
Zhi-Xia Yang
Yuan-Hai Shao
Xiang-Sun Zhang
Publikationsdatum
01.05.2013
Verlag
Springer-Verlag
Erschienen in
Neural Computing and Applications / Ausgabe Sonderheft 1/2013
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-012-1108-x

Weitere Artikel der Sonderheft 1/2013

Neural Computing and Applications 1/2013 Zur Ausgabe