Skip to main content
SpringerLink
Log in

Multi-class support vector machine based on the minimization of class variance

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Since the existing methods can not balance the sufficient use of information and the scale of the optimization problem, a new method for multi class classification problem is proposed, which is called multi-class support vector machine based on the minimization of class variance (MCVMSVM for short). MCVMSVM adopts the idea of semi-supervised learning and transfers the K-class problem to K(K − 1)/2 binary classification problems. For each binary classification problem, a new SVM with a mixed regularization term which considers the margin and the distribution of examples is proposed. MCVMSVM can utilize the information of all examples without increasing the scale of the optimization problem. The performance of MCVMSVM on UCI and NDC datasets is the best compared with other methods, that means MCVMSVM is more effective.

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 V (1995) Support-vector network. Mach Learn 20:273–297

    MATH  Google Scholar 

  2. Vapnik V (1998) The nature of statistical learning, 2nd edn. Springer, New York

    MATH  Google Scholar 

  3. Bennett KP (1999) Combining support vector and mathematical programming methods for classification. In: Schälkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods: support vector learning. MIT Press, Cambridge, MA, pp 307–326

    Google Scholar 

  4. Lee Y, Lin Y, Wahba G (2001) Multicategory support vector machines. Comput Sci Stat 33:498–512

    Google Scholar 

  5. Weston J, Watkins C (1998) Multi-class support vector machines, CSD-TR-98-04 Royal Holloway. University of London, Egham, UK

    Google Scholar 

  6. Graepel T, et al (1999) Classification on proximity data with LP-machines, In: Ninth International Conference on Artifical Neural Networks IEEE, London: Conference Publications, pp. 304–309.

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

    Article  Google Scholar 

  8. Crammer K, Singer Y (2002) On the algorithmic implementation of multiclass kernel-based vector machines. J Mach Learn Res 2:265–292

    MATH  Google Scholar 

  9. Bottou L, Cortes C, Denker JS, Drucher H, Guyon I, Jackel LD, LeCun Y, Muller UA, Sackinger E, Simard P, Vapnik V (1994) Comparison of classifier methods: a case study in handwriting digit recognition. In: International Conference on Pattern Recognition, Vol 2-conference B: Computer Vision & Image Processing

  10. Kreb U (1999) Pairwise classification and support vector machines. In: Scholkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel methods: support vector learning. MIT Press, Cambridge, pp 255–268

    Google Scholar 

  11. Angulo C, Parra X, Catala A (2003) K-SVCR. A support vector machine for multi-class classification. Nurocomputing 55(1):57–77

    Article  Google Scholar 

  12. Yang X, Shao YH (2013) Multiple birth support vector machine for multi-class classification. Neural Comput Appl 22(Suppl 1):S153–S216

    Article  MathSciNet  Google Scholar 

  13. Deng NY, Tian YJ (2012) Support vector machines: optimization based theory, algorithms, and extensions. CRC Press, Boca Raton

    Book  Google Scholar 

  14. Kotsia I, Zafeiriou S, Pitas I (2009) Novel multiclass classifiers based on the minimization of the within class variance. IEEE Trans Neural Netw 20(1):14–34

    Article  Google Scholar 

  15. Blake C, Merz C (1998) UCI repository for machine learning databases. http://www.ics.uci.edu/mlearn/MLRepository.html

  16. Lu J, Xuan JY, Zhang GP (2018) Structural property-aware multilayer network embedding for latent factor analysis. Pattern Recognit 76:228–241

    Article  Google Scholar 

  17. Sun B, Wen SP, Wang SB (2019) Quantized synchronization of memristor-based neural networks via super twisting algorithm. Neurocomputing 380:133–140

    Article  Google Scholar 

  18. Sun B, Cao YT, Guo ZY (2020) Synchronization of discrete-time recurrent neural networks with time-varying delays via quantized sliding mode control. Appl Math Comput 375:125093

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Zhiqiang Zhang

  2. College of Science, China Agricultural University, Beijing, 100083, China

    Zeqian Xu, Junyan Tan & Hui Zou

Authors
  1. Zhiqiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeqian Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junyan Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Junyan Tan or Hui Zou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Xu, Z., Tan, J. et al. Multi-class support vector machine based on the minimization of class variance. Neural Process Lett 53, 517–533 (2021). https://doi.org/10.1007/s11063-020-10393-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-020-10393-7

Keywords

Search

Navigation