Skip to main content
SpringerLink
Log in

ν-Nonparallel support vector machine for pattern classification

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, we propose a novel nonparallel hyperplane classifier, named ν-nonparallel support vector machine (ν-NPSVM), for binary classification. Based on our recently proposed method, i.e., nonparallel support vector machine (NPSVM), which has been proved superior to the twin support vector machines, ν-NPSVM is parameterized by the quantity ν to let ones effectively control the number of support vectors. By combining the ν-support vector classification and the ν-support vector regression together to construct the primal problems, ν-NPSVM inherits the advantages of ν-support vector machine so that enables us to eliminate one of the other free parameters of the NPSVM: the accuracy parameter ε and the regularization constant C. We describe the algorithm, give some theoretical results concerning the meaning and the choice of ν, and also report the experimental results on lots of data sets to show the effectiveness of our method.

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

Access this article

Log in via an institution

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Vapnik VN (1996) The nature of statistical learning theory. Springer, New York

    Google Scholar 

  3. Vapnik VN (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  4. Burges C (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2:121–167

    Article  Google Scholar 

  5. Deng NY, Tian YJ, Zhang CH (2012) Support vector machines: optimization based theory, algorithms, and extensions. Chapman and Hall/CRC, London

    Google Scholar 

  6. Trafalis TB, Ince H (2000) Support vector machine for regression and applications to financial forecasting. In: Proceedings of IEEE-INNSENNS international joint conference neural networks, vol 6, pp 348–353

  7. Li S, Kwok JT, Zhu H, Wang Y (2003) Texture classification using the support vector machines. Pattern Recogn 36(12):2883–2893

    Article  MATH  Google Scholar 

  8. Wu YC, Lee YS, Yang JC (2008) Robust and efficient multiclass SVM models for phrase pattern recognition. Pattern Recogn 41(9):2874–2889

    Article  MATH  Google Scholar 

  9. Isa D, Lee LH, Kallimani VP, RajKumar R (2008) Text document preprocessing with the Bayes formula for classification using the support vector machine. IEEE Trans Knowl Data Eng 20(9):1264–1272

    Article  Google Scholar 

  10. Karsten MB (2011) Kernel methods in bioinformatics. Handb Stat Bioinform Part 3:317–334

    Google Scholar 

  11. Wang XY, Wang T, Bu J (2011) Color image segmentation using pixel wise support vector machine classification. Pattern Recogn 44(4):777–787

    Article  MATH  Google Scholar 

  12. Khan N, Ksantini R, Ahmad I, Boufama B (2012) A novel SVM+ NDA model for classification with an application to face recognition. Pattern Recogn 45(1):66–79

    Article  MATH  Google Scholar 

  13. 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 

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

    Article  Google Scholar 

  15. Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recogn Lett 29(13):1842–1848

    Article  Google Scholar 

  16. Khemchandani R, Jayadeva RK, Chandra S (2009) Optimal kernel selection in twin support vector machines. Optim Lett 3(1):77–88

    Article  MathSciNet  MATH  Google Scholar 

  17. Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36(4):7535–7543

    Article  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. Shao YH, Deng NY (2013) A novel margin-based twin support vector machine with unity norm hyperplanes. Neural Comput Appl 22:1627–1635

    Article  Google Scholar 

  20. Shao Y-H, Deng N-Y (2012) A coordinate descent margin based-twin support vector machine for classification. Neural Netw 25:114–121

    Article  MATH  Google Scholar 

  21. Peng XJ (2010) Tsvr: An efficient twin support vector machine for regression. Neural Netw 23(3):365–372

    Article  Google Scholar 

  22. Chen X, Yang J, Ye Q, Liang J (2011) Recursive projection twin support vector machine via within-class variance minimization. Pattern Recogn. doi:10.1016/j.patcog.2011.03.001

  23. Qi ZQ, Tian YJ, Shi Y (2012) Laplacian twin support vector machine for semi-supervised classification. Neural Netw 35:46–53

    Article  MATH  Google Scholar 

  24. Qi ZQ, Tian YJ, Shi Y (2012) Twin support vector machine with universum data. Neural Netw 36:112–119

    Article  MATH  Google Scholar 

  25. Qi ZQ, Tian YJ, Shi Y (2013) Robust twin support vector machine for pattern classification. Pattern Recogn 46:305–316

    Article  MATH  Google Scholar 

  26. Qi ZQ, Tian YJ, Shi Y (2013) Structural twin support vector machine for classification. Knowl-Based Syst 43:74–81

    Article  Google Scholar 

  27. Tian YJ, Shi Y, Liu XH (2012) Recent advances on support vector machines research. Technol Econ Dev Econ 18:5–33

    Article  Google Scholar 

  28. Tian YJ, Ju XC, Qi ZQ (2013) Efficient sparse nonparallel support vector machines for classification. Neural Comput Appl. doi:10.1007/s00521-012-1331-5

  29. Tian YJ, Qi ZQ, Ju XC, Shi Y, Liu XH (2013) Nonparallel support vector machines for pattern classification. IEEE Trans Cybern. doi:10.1109/TCYB.2013.2279167

  30. Tian YJ, Ju XC, Qi ZQ, Shi Y (2013) Improved twin support vector machine. Sci China Math. doi:10.1007/s11425-013-4718-6

  31. Platt J (2000) 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

    Google Scholar 

  32. Williamson RC, Scholkopf B, Smola A, Bartlett PL (2000) New support vector algorithms. Neural Comput 12:1207–1245

    Article  Google Scholar 

  33. Blake CL, Merz CJ (1998) UCI repository for machine learning databases. Department of Information and Computer Science, University of California, Irvine (Online). http://www.ics.uci.edu/~mlearn/MLRepository.html

Download references

Acknowledgments

This work has been partially supported by grants from National Natural Science Foundation of China (Nos. 11271361, 71331005), the CAS/SAFEA International Partnership Program for Creative Research Teams, Major International (Regional) Joint Research Project (No. 71110107026), and the Ministry of water resources’ special funds for scientific research on public causes (No. 201301094).

Author information

Authors and Affiliations

  1. Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yingjie Tian & Qin Zhang

  2. Department of Basic Course Teaching, Beijing Union University, Beijing, 100101, China

    Dalian Liu

Authors
  1. Yingjie Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dalian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dalian Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian, Y., Zhang, Q. & Liu, D. ν-Nonparallel support vector machine for pattern classification. Neural Comput & Applic 25, 1007–1020 (2014). https://doi.org/10.1007/s00521-014-1575-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-014-1575-3

Keywords

Search

Navigation