Skip to main content

Advertisement

Springer Nature Link
Log in

Robust Pinball Twin Bounded Support Vector Machine for Data Classification

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, a novel robust \(L_{1}\)-norm based twin bounded support vector machine with pinball loss- having regularization term, scatter loss and misclassification loss- is proposed to enhance robustness in the presence of feature noise and outliers. Unlike in twin bounded support vector machine (TBSVM), pinball is used as the misclassification loss in place of hinge loss to reduce noise sensitivity. To further boost robustness, the scatter loss of the class of vectors is minimized using \(L_{1}\)-norm. As an equivalent problem in simple form, a pair of quadratic programming problems (QPPs) is constructed (L1-Pin-TBSVM) with m variables where m is the number of training vectors. Unlike TBSVM, the proposed L1-Pin-TBSVM is free from inverse kernel matrix and the non-linear problem can be obtained directly from its linear formulation by applying the kernel trick. The efficacy and robustness of L1-Pin-TBSVM has been demonstrated by experiments performed on synthetic and UCI datasets in the presence of noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Cortes C, Vapnik VN (1995) Support-vector networks. Mach Learn 20(3):273–297

    Article  MATH  Google Scholar 

  2. Vapnik VN (2000) The nature of statistical learning theory, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  3. Guyon I, Weston J, Barnhill S, Vapnik VN (2002) Gene selection for cancer classification using support vector machine. Mach Learn 46:389–422

    Article  MATH  Google Scholar 

  4. Joachims T, Ndellec C,.Rouveriol C (1998) Text categorization with support vector machines: learning with many elevant features. In: European conference on machine learning, No.10, Chemnitz, Germany, pp 137–142

  5. Kim SK, Park YJ, Toh KA, Lee S (2010) SVM-based feature extraction for face recognition. Pattern Recogn 43(8):2871–2881

    Article  MATH  Google Scholar 

  6. Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel based learning method. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  7. Osuna F,.Freund R,.Girosi F (1997) An improved training algorithm for support vector machines. In: Proceedings of the IEEE workshop on neural networks for signal processing, Amelia Island, FL, pp 276–285

  8. Platt J (1999) Fast training of support vector machines using sequential minimal optimization, Advances in Kernel Methods-Support Vector Learning, MIT Press, Cambridge. MA, pp 185–208

  9. Hsieh C-J, Chang K-W, Lin C-J (2008) A dual coordinate descent method for large scale linear SVM. In: Proceedings of the 25th international conference on machine learning, Helsinki

  10. Mangasarian OL, Musicant DR (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Networks 10(5):1032–1037

    Article  Google Scholar 

  11. Mangasarian OL, Wild EW (2006) Multisurface proximal support vector classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74

    Article  Google Scholar 

  12. Jayadeva R, Khemchandani S (2007) Chandra, Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910

    Article  MATH  Google Scholar 

  13. Balasundaram S, Gupta D, Prasad SC (2017) A new approach for training Lagrangian twin support vector machine via unconstrained convex minimization. Appl Intell 46:124–134

    Article  Google Scholar 

  14. Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36:7535–7543

    Article  Google Scholar 

  15. Peng X (2010) A ν-twin support vector machine (ν-TSVM) classifier and its geometric algorithms. Inf Sci 180(20):3863–3875

    Article  MathSciNet  MATH  Google Scholar 

  16. Peng X (2011) TPMSVM: a novel twin parametric-margin support vector machine for pattern recognition. Pattern Recogn 44(10–11):2678–2692

    Article  MATH  Google Scholar 

  17. Peng X, Xu D, Kong L, Chen D (2016) norm based twin support vector machine for data recognition. Inf Sci 340–341:86–103

    Article  MathSciNet  MATH  Google Scholar 

  18. Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968

    Article  Google Scholar 

  19. Huang X, Shi L, Suykens JAK (2014) Support vector machine classifier with pinball loss. IEEE Trans Pattern Anal Mach Intell 5:984–997

    Article  Google Scholar 

  20. Rastogi R, Pal A, Chandra S (2018) Generalized Pinball loss SVMs. Neurocomputing 322:151–165

    Article  Google Scholar 

  21. Xu Y, Yang Z, Pan X (2016) A novel twin support-vector machine with pinball loss. IEEE Trans Neural Netw Learn Syst 28(2):359–370

    Article  MathSciNet  Google Scholar 

  22. Huang X, Shi L, Suykens JAK (2014) Asymmetric least squares support vector machine classifiers. Comput Stat Data Anal 70:395–405

    Article  MathSciNet  MATH  Google Scholar 

  23. Prasad SC, Balasundaram S (2021) On Lagrangian L2-norm pinball twin bounded support vector machine via unconstrained convex minimization. Inf Sci 571:279–302

    Article  MathSciNet  Google Scholar 

  24. Frenay B, Verleysen M (2014) Classification in the presence of label noise: a survey. IEEE Trans Neural Netw Learn Syst 25(5):845–869

    Article  MATH  Google Scholar 

  25. Suykens JAK, Brabanter JD, Lukas L, Vandewalle J (2002) Weighted least squares support vector machine: robustness and sparse approximation. Neurocomputing 48(1):85–105

    Article  MATH  Google Scholar 

  26. Mehrkanoon S, Huang X, Suykens JAK (2014) Non-parallel support vector classifiers with different loss functions. Neurocomputing 143:294–301

    Article  Google Scholar 

  27. Yang L, Dong H (2018) Support vector machine with truncated pinball loss and its application in pattern recognition. Chemom Intell Lab Syst 177:89–99

    Article  Google Scholar 

  28. Huang X, Shi L, Suykens JAK (2014) Ramp loss linear programming support vector machine. J Mach Learn Res 15:2185–2211

    MathSciNet  MATH  Google Scholar 

  29. Shen X, Niu L, Qi Z, Tian Y (2017) Support vector machine classifier with truncated pinball loss. Pattern Recogn 68:199–210

    Article  Google Scholar 

  30. Gao S, Ye Q, Ye N (2011) 1-norm least squares twin support vector machines. Neurocomputing 74:3590–3597

    Article  Google Scholar 

  31. Yan H, Ye Q, Zhang T, Yu D-J, Yuan X, Xu Y, Fu L (2018) Least squares twin bounded support vector machines based on L1-norm distance metric for classification. Pattern Recognit 74:434–447

    Article  Google Scholar 

  32. Yan H, Ye Q-L, Yu D-J (2019) Efficient and robust TWSVM classification via a minimum L1-norm distance metric criterion. Mach Learn 108:993–1018

    Article  MathSciNet  MATH  Google Scholar 

  33. Hao P-Y (2010) New support vector algorithms with parametric insensitive/margin model. Neural Netw 23(1):60–73

    Article  MATH  Google Scholar 

  34. Peng X, Chen D, Kong L (2014) A clipping dual coordinate descent algorithm for solving support vector machines. Knowl-Bases Syst 71:266–278

    Article  Google Scholar 

  35. Murphy PM, Aha DW (1992) UCI repository of machine learning databases. University of California, Irvine. http://www.ics.uci.edu/~mlearn

  36. Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Lear Res 7:1–30

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are very thankful to the reviewers for their valuable comments which helped improve the presentation of the paper significantly.

Author information

Authors and Affiliations

  1. School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi, 110067, India

    Subhash Chandra Prasad, P. Anagha & S. Balasundaram

Authors
  1. Subhash Chandra Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Anagha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Balasundaram
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Balasundaram.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prasad, S.C., Anagha, P. & Balasundaram, S. Robust Pinball Twin Bounded Support Vector Machine for Data Classification. Neural Process Lett 55, 1131–1153 (2023). https://doi.org/10.1007/s11063-022-10930-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10930-6

Keywords