A Non-singular Twin Support Vector Machine

  • Wu QingEmail author
  • Qi Shaowei
  • Zhang Haoyi
  • Jing Rongrong
  • Miao Jianchen
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 891)


Due to high efficiency, twin support vector machine (TWSVM) is suitable for large-scale classification problems. However, there is a singularity in solving the quadratic programming problems (QPPs). In order to overcome it, a new method to solve the QPPs is proposed in this paper, named non-singular twin support vector machine (NSTWSVM). We introduce a nonzero term to the result of the problem. Compared to the TWSVM, it does not need extra parameters. In addition, the successive overrelaxation technique is adopted to solve the QPPs in the NSTWSVM algorithm to speed up the training procedure. Experimental results show the effectiveness of the proposed method in both computation time and accuracy.


Twin support vector machine Singularity Classification 



This work was supported in part by the National Natural Science Foundation of China under Grants (61472307, 51405387), the Key Research Project of Shaanxi Province (2018GY-018) and the Foundation of Education Department of Shaanxi Province (17JK0713).


  1. 1.
    Cortes, C., Vapnik, V.: Support vector networks. Mach. Learn. 20(3), 273–297 (1995). Scholar
  2. 2.
    Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1996). Scholar
  3. 3.
    Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)zbMATHGoogle Scholar
  4. 4.
    Chen, S., Wu, X.: Improved projection twin support vector machine. ACTA Electron. Sinca 45(2), 408–416 (2017). Scholar
  5. 5.
    Qi, Z., Tian, Y., Shi, Y.: Robust twin support vector machine for pattern classification. Pattern Recognit. 46(1), 305–316 (2013). Scholar
  6. 6.
    Chen, S., Wu, X.: A new fuzzy twin support vector machine for pattern classification. Int. J. Mach. Learn. Cybern. 3, 1–12 (2017). Scholar
  7. 7.
    Tanveer, M., Khan, M., Ho, S.: Robust energy-based least squares twin support vector machines. Appl. Intell. 45(1), 174–186 (2016). Scholar
  8. 8.
    Borgwardt, K.: Kernel methods in bioinformatics. Springer, Berlin Heidelberg (2011). Scholar
  9. 9.
    Kumar, M., Gopal, M.: Least squares twin support vector machines for pattern classification. Expert Syst. Appl. Int. J. 36(4), 7535–7543 (2009). Scholar
  10. 10.
    Hao, P., Chiang, J., Lin, Y.: A new maximal-margin spherical-structured multi-class support vector machine. Appl. Intell. 30(2), 98–111 (2009). Scholar
  11. 11.
    Mangasarian, O., Wild, E.: Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 69–74 (2006). Scholar
  12. 12.
    Jayadeva, R., Khemchandani, R., Chandra, S.: Twin support vector machines for pattern classification. IEEE Trans. Pattern Anal. Mach. Intell. 29(5), 905–910 (2007). Scholar
  13. 13.
    Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  14. 14.
    Zhang, C., Tian, Y., Deng, N.: The new interpretation of support vector machines on statistical. Sci. Chin. Math. 53(1), 151–164 (2010). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Wu Qing
    • 1
    Email author
  • Qi Shaowei
    • 1
  • Zhang Haoyi
    • 1
  • Jing Rongrong
    • 1
  • Miao Jianchen
    • 1
  1. 1.School of AutomationXi’an University of Posts and TelecommunicationsXi’anChina

Personalised recommendations