A new fuzzy twin support vector machine for pattern classification

  • Su-Gen Chen
  • Xiao-Jun WuEmail author
Original Article


Fuzzy SVM is often used to solve the problem that patterns belonging to one class often play more significant roles in classification. In order to improve the efficiency and performance of fuzzy SVM, this paper proposes a new fuzzy twin support vector machine (NFTSVM) for binary classification, in which fuzzy neural networks and twin support vector machine (TWSVM) are incorporated. By design, the influence of the samples with high uncertainty can be mitigated by employing fuzzy membership to weigh the margin of each training sample, which improves the generalization ability. In addition, we show that the existing TWSVM and twin bounded support vector machines (TBSVM) are special cases of the proposed NFTSVM when the parameters of NFTSVM are appropriately selected. Moreover, the successive overrelaxation (SOR) technique is adopted to solve the quadratic programming problems (QPPs) in the proposed NFTSVM algorithm to speed up the training procedure. Experimental results obtained on several artificial and real-world datasets validate the feasibility and effectiveness of the proposed method.


Pattern classification Twin support vector machine Fuzzy support vector machine Successive overrelaxation technique 



This work was partially supported by the National Natural Science Foundation of China (Grant No. 61373055 and 61672265), the University Natural Science Research Project of Anhui Province of China (Grant No. KJ2015A266, KJ2016A431 and KJ2017A361) and the University Outstanding Young Talent Support Project of Anhui Province of China (Grant No. gxyq2017026).


  1. 1.
    Cortes C, Vapnik VN (1995) Support vector machine. Mach Learn 20(3):273–297zbMATHGoogle Scholar
  2. 2.
    Vapnik VN (2000) The nature of statistical learning theory. Springer-Verlag, New York (Incorporated)CrossRefzbMATHGoogle Scholar
  3. 3.
    Burges C (1998) A tutorial support vector machines for pattern recognition. Data Min Knowl Disc 2:1–43CrossRefGoogle Scholar
  4. 4.
    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):1264–1272CrossRefGoogle Scholar
  5. 5.
    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):77–87CrossRefGoogle Scholar
  6. 6.
    You ZH, Yu JZ, Zhu L, Li S, Wen ZK (2014) A mapreduce based parallel SVM for large-scale predicting protein–protein interactions. Neurocomputing 145: 37–43CrossRefGoogle Scholar
  7. 7.
    Mangasarian OL, Wild EW (2006) Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRefGoogle Scholar
  8. 8.
    Jayadeva, R Khemchandani, S Chandra (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRefzbMATHGoogle Scholar
  9. 9.
    Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36(4):7535–7543CrossRefGoogle Scholar
  10. 10.
    Shao YH, Zhang CH, Wang XB, Deng NY (2011) Improvements on twin support vector machines. IEEE Trans Neural Networks 22(6):962–968CrossRefGoogle Scholar
  11. 11.
    Peng XJ (2011) TPMSVM: a novel twin parametric-margin support vector machine for pattern recognition. Pattern Recognit 44(10):2678–2692CrossRefzbMATHGoogle Scholar
  12. 12.
    Qi ZQ, Tian YJ, Shi Y (2013) Robust twin support vector machine for pattern classification. Pattern Recognit 46(1):305–316CrossRefzbMATHGoogle Scholar
  13. 13.
    Wang Z, Shao YH, Wu TR (2014) Proximal parametric-margin support vector classifier and its applications. Neural Comput Applic 24:755–764CrossRefGoogle Scholar
  14. 14.
    Shao YH, Chen WJ, Deng NY (2014) Nonparallel hyperplane support vector machine for binary classification problems. Inf Sci 263:22–35MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Tian YJ, Qi ZQ, Ju XC, Shi Y, Liu XH (2014) Nonparallel support vector machines for pattern classification. IEEE Trans on Cybern 44(7):1067–1079CrossRefGoogle Scholar
  16. 16.
    Chen SG, Wu XJ, Zhang RF (2016) A novel twin support vector machine for binary classification problems. Neural Process Lett 44(3):795–811CrossRefGoogle Scholar
  17. 17.
    Ye QL, Zhao CX, N. Y, Chen YN (2010) Multi-weight vector projection support vector machines. Pattern Recognit Lett 31:2006–2011CrossRefGoogle Scholar
  18. 18.
    Chen XB, Yang J, Ye QL, Liang J (2011) Recursive projection twin support vector machine via within-class variance minimization. Pattern Recognit 44(10):2643–2655CrossRefzbMATHGoogle Scholar
  19. 19.
    Shao YH, Deng NY, Yang ZM (2012) Least squares recursive projection twin support vector machine for classification. Pattern Recognit 45(6):2299–2307CrossRefzbMATHGoogle Scholar
  20. 20.
    Ding SF, Hua XP (2014) Recursive least squares projection twin support vector machines for nonlinear classification. Neurocomputing 130: 3–9CrossRefGoogle Scholar
  21. 21.
    Ding SF, JZ Yu, BJ Qi (2014) An overview on twin support vector machines. Artif Intell Rev 42(2):245–252CrossRefGoogle Scholar
  22. 22.
    Lin CF, Wang SD (2002) Fuzzy support vector machines. IEEE Trans Neural Networks 13(2):464–471CrossRefGoogle Scholar
  23. 23.
    Jiang XF, Yi Z, Lv JC (2006) Fuzzy SVM with a new fuzzy membership function. Neural Comput Appl 15(3–4):268–276CrossRefGoogle Scholar
  24. 24.
    An WJ, Liang MG (2013) Fuzzy support vector machine based on within-class scatter for classification problems with outliers or noises. Neurocomputing 110(7):101–110CrossRefGoogle Scholar
  25. 25.
    Ding SF, Han YZ, JZ Yu, YX Gu (2013) A fast fuzzy support vector machine based on information granulation. Neural Comput Appl 23:139–144CrossRefGoogle Scholar
  26. 26.
    Wang XZ, RAR Ashfaq, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196MathSciNetCrossRefGoogle Scholar
  27. 27.
    Keller JM, Hunt DJ (1985) Incorporating fuzzy membership functions into the perceptron algorithm. IEEE Trans Pattern Anal Mach Intell 6:693–699CrossRefGoogle Scholar
  28. 28.
    Tao Q, Wang J (2004) A new fuzzy support vector machine based on the weighted margin. Neural Process Lett 20(3):139–150CrossRefGoogle Scholar
  29. 29.
    Khemchandani R, Jayadeva, Chandra S (2008) Fuzzy twin support vector machines for pattern classification. Mathematical programming and game theory for decision making. World Scientific, Singapore, pp 131–142CrossRefzbMATHGoogle Scholar
  30. 30.
    Li K, Ma HY (2013) A fuzzy twin support vector machine algorithm. Int J Appl Innov Eng Manag 2(3):459–465Google Scholar
  31. 31.
    R.O. Duda, P.E. Hart, D.G. Stork (2001) Pattern classification. Second edition, Wiley, HobokenzbMATHGoogle Scholar
  32. 32.
    Mangasarian OL, Musicant DR (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Networks 10(5):1032–1037CrossRefGoogle Scholar
  33. 33.
    Lee YJ, Huang SY (2007) Reduced support vector machines: a statistical theory. IEEE Trans Neural Networks 13(1):1–13CrossRefGoogle Scholar
  34. 34.
    Ripley BD (2008) Pattern recognition and neural networks. Cambridge University, CambridgezbMATHGoogle Scholar
  35. 35.
    Muphy PM, Aha DW (1992) UCI repository of machine learning databases. University of California, Irvine.
  36. 36.
  37. 37.
    Nene SA, Nayar SK, Murase H (1996) Columbia object image library (COIL-20). Technical report CUCS-005-96, Department of Computer Science, Columbia UniversityGoogle Scholar
  38. 38.
    Martinez AM, Benavente R (1998) The AR face database. CVC Technical Report #24Google Scholar
  39. 39.
    Wang XZ, He Q, Chen DG, Yeung D (2005) A genetic algorithm for solving the inverse problem of support vector machines. Neurocomputing 68: 225–238CrossRefGoogle Scholar
  40. 40.
    Wang XZ, Lu SX, Zhai JH (2008) Fast fuzzy multi-category SVM based on support vector domain description. Int J Pattern Recognit Artif Intell 22(1):109–120CrossRefGoogle Scholar
  41. 41.
    Wang XZ (2015) Uncertainty in learning from big data-Editorial. J Intell Fuzzy Syst 28(5):2329–2330CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of IoT EngineeringJiangnan UniversityWuxiPeople’s Republic of China
  2. 2.School of Mathematics and Computational ScienceAnqing Normal UniversityAnqingPeople’s Republic of China

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