Advertisement

Soft Computing

, Volume 23, Issue 2, pp 655–668 | Cite as

A novel projection twin support vector machine for binary classification

  • Sugen Chen
  • Xiaojun WuEmail author
  • Hefeng Yin
Methodologies and Application
  • 159 Downloads

Abstract

Based on the recently proposed projection twin support vector machine (PTSVM) and projection twin support vector machine with regularization term (RPTSVM), we propose a novel projection twin support vector machine (NPTSVM) for binary classification problems. Our proposed NPTSVM seeks two optimal projection directions simultaneously by solving a single quadratic programming problem, and the projected samples of one class are well separated from those of another class to some extent. Similar to RPTSVM, the singularity of matrix is avoided and the structural risk minimization principle is implemented in our NPTSVM. In addition, in our NPTSVM, we also discuss the nonlinear classification scenario which is not covered in PTSVM. The experimental results on several artificial and publicly available benchmark datasets show the feasibility and effectiveness of the proposed method.

Keywords

Machine learning Binary classification Twin support vector machine Projection twin support vector machine Successive overrelaxation technique 

Notes

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 61373055, 61672265 and 61702012), the University Outstanding Young Talent Support Project of Anhui Province of China (Grant No. gxyq2017026) and the University Natural Science Research Project of Anhui Province of China (Grant Nos. KJ2016A431, KJ2017A361 and KJ2017A368).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

  1. Byun H, Lee SW (2002) Applications of support vector machines for pattern recognition: a survey. Pattern recognition with support vector machines. Springer, Berlin, pp 213–236zbMATHGoogle Scholar
  2. Chang C, Lin C (2001) LIBSVM: a library for support vector machine. Technical report, Department of Computer Science and Information Engineering, National Taiwan UniversityGoogle Scholar
  3. Chen XB, Yang J, Ye QL, Liang J (2011) Recursive projection twin support vector machine via within-class variance minimization. Pattern Recogn 44(10):2643–2655zbMATHGoogle Scholar
  4. Chen SG, Wu XJ, Zhang RF (2016) A novel twin support vector machine for binary classification problems. Neural Process Lett 263:22–35Google Scholar
  5. Cheng CT, Wang WC, Xu DM et al (2008) Optimizing hydropower reservoir operation using hybrid genetic algorithm and chaos. Water Resour Manag 22(7):895–909Google Scholar
  6. Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20:273–297zbMATHGoogle Scholar
  7. Ding SF, Hua XP (2014) Recursive least squares projection twin support vector machines for nonlinear classification. Neurocomputing 130:3–9Google Scholar
  8. Ding SF, Yu JZ, Qi BJ, Huang HJ (2014) An overview on twin support vector machines. Artif Intell Rev 42(2):245–252Google Scholar
  9. Duda GH, Van Loan CF (1996) Matrix computations, vol 3. Johns Hopkins University Press, BaltimoreGoogle Scholar
  10. Duda DO, Hart PE, Stork DG (2001) Pattern classification, Second edn. Wiley, New YorkzbMATHGoogle Scholar
  11. Fung G, Mangasarian OL (2005) Multicategory proximal support vector machine classifiers. Mach Learn 59:77–97zbMATHGoogle Scholar
  12. Khemchandani JR, Chandra R (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910zbMATHGoogle Scholar
  13. Lee YJ, Huang SY (2007) Reduced support vector machines: a statistical theory. IEEE Trans Neural Netw 13(1):1–13Google Scholar
  14. Mangasarian OL (1994) Nonlinear programming. SIAM, New DelhizbMATHGoogle Scholar
  15. Mangasarian OL, Musicant DR (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Netw 10(5):1032–1037Google Scholar
  16. Mangasarian OL, Wild EW (2006) Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74Google Scholar
  17. Muphy PM, Aha DW (1992) UCI repository of machine learning databases. University of California, Irvine. http://www.ics.uci.edu/~mlearn
  18. Peng XJ (2011) TPMSVM: a novel twin parametric-margin support vector machine for pattern recognition. Pattern Recogn 44(10):2678–2692zbMATHGoogle Scholar
  19. Peng XJ, Xu D (2012) Twin Mahalanobis distance-based support vector machines for pattern recognition. Inf Sci 200:22–37MathSciNetzbMATHGoogle Scholar
  20. Peng XJ, Xu D (2013) Robust minimum class variance twin support vector machine classifier. Neural Comput Appl 22(5):999–1011Google Scholar
  21. Peng XJ, Xu D (2014) Twin support vector hypersphere (TSVH) classifier for pattern recognition. Neural Comput Appl 24:1207–1220Google Scholar
  22. Platt J (1999) Fast training of support vector machines using sequential minimal optimization. In: Scholkopf B, Burges CJC, Smola AJ (eds) Advances in kernel methods-support vector learning. MIT Press, Cambridge, pp 185–208Google Scholar
  23. Qi ZQ, Tian YJ, Shi Y (2013a) Robust twin support vector machine for pattern classification. Pattern Recogn 46(1):305–316zbMATHGoogle Scholar
  24. Qi ZQ, Tian YJ, Shi Y (2013b) Structural twin support vector machine for classification. Knowl Based Syst 43:74–81Google Scholar
  25. Ripley BD (2008) Pattern recognition and neural networks. Cambridge University Press, CambridgezbMATHGoogle Scholar
  26. Shao YH, Deng NY (2012) A coordinate descent margin based-twin support vector machine for classification. Neural Netw 25:114–121zbMATHGoogle Scholar
  27. Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968Google Scholar
  28. Shao YH, Deng NY, Yang ZM (2012) Least squares recursive projection twin support vector machine for classification. Pattern Recogn 45(6):2299–2307zbMATHGoogle Scholar
  29. Shao YH, Wang Z, Chen WJ, Deng NY (2013) A regularization for the projection twin support vector machine. Knowl Based Syst 37:203–210Google Scholar
  30. Shao YH, Chen WJ, Deng NY (2014) Nonparallel hyperplane support vector machine for binary classification problems. Inf Sci 263:22–35MathSciNetzbMATHGoogle Scholar
  31. Sun J, Fang W, Wu XJ, Palade P, Xu WB (2012) Quantum-behaved particle swarm optimization: analysis of individual particle behavior and parameter selection. Evol Comput 20(3):349–393Google Scholar
  32. Suykens J, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9:293–300Google Scholar
  33. Trafails TB, Ince H (2002) Support vector machine for regression and applications to financial forecasting. In: IEEE-INNS-ENNS international joint conference on neural networks, IEEE computer society, vol 6, pp 6348–6348Google Scholar
  34. Vapnik VN (2000) The nature of statistical learning theory. Springer, New YorkzbMATHGoogle Scholar
  35. Wang R, Kwong S, Chen DG, Cao JJ (2013) A vector-valued support vector machine model for multi-class problem. Inf Sci 235:174–194zbMATHGoogle Scholar
  36. Ye QL, Zhao CX, Ye N, Chen YN (2010) Multi-weight vector projection support vector machines. Pattern Recogn Lett 31:2006–2011Google Scholar
  37. Yen SJ, Wu YC, Yang JC, Lee YS, Liu LL (2013) A support vector machine-based context-ranking model for question answering. Inf Sci 224(1):77–87Google Scholar
  38. Zhang J, Chau KW (2009) Multilayer ensemble pruning via novel multi-sub-swarm particle swarm optimization. J Univ Comput Sci 15(4):840–858Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceAnqing Normal UniversityAnqingPeople’s Republic of China
  2. 2.School of IoT EngineeringJiangnan UniversityWuxiPeople’s Republic of China
  3. 3.Centre for Vision, Speech and Signal ProcessingUniversity of SurreyGuildfordUK

Personalised recommendations