Skip to main content
SpringerLink
Log in

Online Learning Algorithms for Double-Weighted Least Squares Twin Bounded Support Vector Machines

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Twin support vector machine with two nonparallel classifying hyperplanes and its extensions have attracted much attention in machine learning and data mining. However, the prediction accuracy may be highly influenced when noise is involved. In particular, for the least squares case, the intractable computational burden may be incurred for large scale data. To address the above problems, we propose the double-weighted least squares twin bounded support vector machines and develop the online learning algorithms. By introducing the double-weighted mechanism, the linear and nonlinear double-weighted learning models are proposed to reduce the influence of noise. The online learning algorithms for solving the two models are developed, which can avoid computing the inverse of the large scale matrices. Furthermore, a new pruning mechanism which can avoid updating the kernel matrices in every iteration step for solving nonlinear model is also developed. Simulation results on three UCI data with noise demonstrate that the online learning algorithm for the linear double-weighted learning model can get least computation time as well considerable classification accuracy. Simulation results on UCI data and two-moons data with noise demonstrate that the nonlinear double-weighted learning model can be effectively solved by the online learning algorithm with the pruning mechanism.

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

Similar content being viewed by others

References

  1. Vapnik V (1995) The nature of statistical learning theory. Springer, New York

    Book  MATH  Google Scholar 

  2. Chen X, Yang J, Liang J (2011) Optimal locality regularized least squares support vector machine via alternating optimization. Neural Proces Lett 33(3):301–315

    Article  Google Scholar 

  3. Li G, Meng H, Yang M (2009) Combining support vector regression with feature selection for multivariate calibration. Neural Comput Appl 18(7):813–820

    Article  Google Scholar 

  4. Li J, Jia Y (2010) Huberized multi-class support vector machine for microarray classification. Acta Autom Sin 36:399–405

    MATH  Google Scholar 

  5. Sun C, Mu C, Li X (2009) A weighted LS-SVM approach for the identification of a class of nonlinear inverse systems. Sci China Ser F 52(5):770–779

    Article  MathSciNet  MATH  Google Scholar 

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

  7. Shao Y, Zhang C, Wang X et al (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968

    Article  Google Scholar 

  8. Tian Y, Ju X, Qi Z, Shi Y (2014) Improved twin support vector machine. Sci China Math 57(2):417–432

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun S, Xie X (2015) Semi-supervised support vector machines with tangent space intrinsic manifold regularization. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2015.2461009

  10. Xie X, Sun S (2014) Multi-view Laplacian twin support vector machines. Appl Intell 41:1059–1068

    Article  Google Scholar 

  11. Peng X (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23(3):365–372

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Divya T, Sonali A (2015) A comparison on multi-class classification methods based on least squares twin support vector machine. Knowl-Based Syst 81:131–147

    Article  Google Scholar 

  14. Lin C, Wang S (2002) Fuzzy support vector machines. IEEE Trans Neural Netw 13(2):464–471

    Article  Google Scholar 

  15. Jayadeva R, Khemchandani S, Chandra (2004) Fast and robust learning through fuzzy linear proximal support vector machines. Neurocomputing 61(1–4):401–411

  16. Lin C, Wang S (2004) Training algorithm for fuzzy support vector machines with noisy data. Pattern Recognit Lett 25(14):1647–1656

    Article  Google Scholar 

  17. Subasi A (2012) Medical decision support system for diagnosis of neuromuscular disorders using DWT and fuzzy support vector machines. Comput Biol Med 42(8):806–815

    Article  Google Scholar 

  18. Tang W (2011) Fuzzy SVM with a new fuzzy membership function to solve the two-class problems. Neural Process Lett 34(3):209–219

    Article  Google Scholar 

  19. Yang X, Song Q, Wang Y (2007) A weighted support vector machine for data classification. Int J Pattern Recognit Artif Intell 21(5):961–976

    Article  Google Scholar 

  20. Qi Z, Tian Y, Shi Y (2013) Robust twin support vector machine for pattern classification. Pattern Recognit 46(1):305–316

    Article  MATH  Google Scholar 

  21. Xie X, Sun S (2015) Multitask centroid twin support vector machines. Neurocomputing 149:1085–1091

    Article  Google Scholar 

  22. Wang K, Zhu W, Zhong P (2015) Robust support vector regression with generalized loss function and applications. Neural Process Lett 41:89–106

    Article  Google Scholar 

  23. Ye Q, Zhao C, Gao S, Zheng H (2012) Weighted twin support vector machines with local information and its application. Nerual Netw 35:31–39

    Article  MATH  Google Scholar 

  24. Ye Q, Zhao C, Ye N (2011) Localized twin SVM via convex minimization. Neurocomputing 74(4):580–587

    Article  Google Scholar 

  25. Xu Y, Wang L (2014) K-nearest neighbor-based weighted twin support vector regression. Appl Intell 41(1):299–309

    Article  MathSciNet  Google Scholar 

  26. Li L, Su H, Chu J (2007) Generalized predictive control with online least squares support vector machines. Acta Autom Sin 33(11):1182–1188

    Article  MathSciNet  MATH  Google Scholar 

  27. Yang X, Lu J, Zhang G (2010) Adaptive pruning algorithm for least squares support vector machine classifier. Soft Comput 14(7):667–680

    Article  MATH  Google Scholar 

  28. Wang H, Pi D, Sun Y (2007) Online SVM regression algorithm-based adaptive inverse control. Neurocomputing 70(4–6):952–959

    Article  Google Scholar 

  29. Gu B, Wang J, Yu Y et al (2012) Accurate on-line v-support vector learning. Neural Netw 27:51–59

    Article  MATH  Google Scholar 

  30. Wu Y, Sun S (2015) An online learning algorithm for bilinear models. In: Proceedings of the 32nd international conference on machine learning (ICML), pp 890–898

  31. Ljung L (1999) System identification: theory for the user. Prentice Hall, Englewood Cliffs

    Book  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and insightful suggestions. The authors are also thankful to National Natural Science Foundation of China (61203293, 61374079), Key Scientific and Technological Project of Henan Province (122102210131), Program for Science and Technology Innovation Talents in Universities of Henan Province (13HASTIT040), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (14IRTSTHN023), Henan Higher School Funding Scheme for Young Teachers (2012GGJS-063). Backbone Teachers Program of Henan Normal University.

Author information

Authors and Affiliations

  1. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Juntao Li, Yimin Cao & Yadi Wang

  2. College of Computer and Information Engineering, Henan University of Economics and Law, Zhengzhou, 450002, China

    Huimin Xiao

Authors
  1. Juntao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yimin Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yadi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Huimin Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juntao Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Cao, Y., Wang, Y. et al. Online Learning Algorithms for Double-Weighted Least Squares Twin Bounded Support Vector Machines. Neural Process Lett 45, 319–339 (2017). https://doi.org/10.1007/s11063-016-9527-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-016-9527-9

Keywords

Search

Navigation