Skip to main content
SpringerLink
Log in

A rough ν-twin support vector regression machine

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

After combining the ν-Twin Support Vector Regression (ν-TWSVR) with the rough set theory, we propose an efficient Rough ν-Twin Support Vector Regression, called Rough ν-TWSVR for short. We construct a pair of optimization problems which are motivated by and mathematically derived from a related ν-TWSVR Rastogi et al. (Appl Intell 46(3):670–683 2017) and Rough ν-SVR Zhao et al. (Expert Syst Appl 36(6):9793–9798 2009). Rough ν-TWSVR not only utilizes more data information rather than the extreme data points in the ν-TWSVR, but also makes different points having different effects on the regressor depending on their positions. This method can implement the structural risk minimization and automatically control accuracies according to the structure of the data sets. In addition, the double ε s are utilized to construct the rough tube for upper(lower)-bound Rough ν-TWSVR instead of a single ε in the upper(lower)-bound ν-TWSVR. Moreover, This rough tube consisting of positive region, boundary region, and negative region yields the feasible set of the Rough ν-TWSVR larger than that of the ν-TWSVR, which makes the objective function of the Rough ν-TWSVR no more than that of ν-TWSVR. The Rough ν-TWSVR improves the generalization performance of the ν-TWSVR, especially for the data sets with outliers. Experimental results on toy examples and benchmark data sets confirm the validation and applicability of our proposed Rough ν-TWSVR.

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

Similar content being viewed by others

References

  1. Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297

    MATH  Google Scholar 

  2. Shen C, Wang X (2011) Analysis of convertible bond value based on integration of support vector machine and copula function. Commun Stat Simul Comput 40(10):1563–1575

    Article  MathSciNet  Google Scholar 

  3. Deka PC (2014) Support vector machine applications in the field of hydrology: a review. Appl Soft Comput 19:372–386

    Article  Google Scholar 

  4. Flores MS, Verbraken T et al. (2015) Profit-based feature selection using support vector machines general framework and an application for customer retention. Appl Soft Comput 35:740–748

    Article  Google Scholar 

  5. Schölkopf PB, Burgest C, Vapnik V (1995) Extracting support data for a given task. In: Proceedings of the first international conference on knowledge discovery and data mining. AAAI Press, Menlo Park, pp 252–257

  6. Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222

    Article  MathSciNet  Google Scholar 

  7. Schölkopf B, Bartlett P, Smola A et al. (1998) Support vector regression with automatic accuracy control, ICANN 98. Springer, London, pp 111–116

    Google Scholar 

  8. Vapnik V, Vapnik V (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  9. Deng N, Tian Y, Zhang C (2012) Support vector machines: optimization based theory, algorithms, and extensions. CRC Press, Boca Raton

    Book  Google Scholar 

  10. Suykens JAK, Van Gestel T, De Brabanter J (2002) Least squares support vector machines. World Scientific

  11. Mangasarian OL, Wild EW (2006) Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Shao YH, Zhang C, Wang X, Deng NY (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968

    Article  Google Scholar 

  15. Peng X (2011) TPMSVM: A novel twin parametric-margin support vector machine for pattern recognition. Pattern Recogn 44(10):2678–2692

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Khemchandani R, Goyal K, Chandra S (2016) TWSVR: Regression via twin support vector machine. Neural Netw 74:14–21

    Article  Google Scholar 

  18. Chen X, Yang J, Liang J et al. (2012) Smooth twin support vector regression. Neural Comput Appl 21 (3):505–513

    Article  Google Scholar 

  19. Tanveer M, Shubham K, Aldhaifallah M, Nisar KS (2016) An efficient implicit regularized Lagrangian twin support vector regression. Appl Intell 44(4):831–848

    Article  Google Scholar 

  20. Shao YH, Zhang C, Yang ZM, Jing L, Deng NY (2013) An ε-twin support vector machine for regression. Neural Comput Appl 23(1):175–185

    Article  Google Scholar 

  21. Rastogi R, Anand P, Chandra S (2017) A ν-twin support vector machine based regression with automatic accuracy control. Appl Intell 46(3):670–683

    Article  Google Scholar 

  22. Pawlak Z, Skowron A (2007) Rough sets and Boolean reasoning. Information rough 177(1):41–73. Sciences 177(2007) 21–73

    MathSciNet  MATH  Google Scholar 

  23. Law Pawlak Z (2002) Rough sets and intelligent data analysis. Inf Sci 147(1):1–12

    Article  MathSciNet  Google Scholar 

  24. Chen RC, Cheng KF, Chen YH et al. (2009) Using rough set and support vector machine for network intrusion detection system. In: First Asian conference on intelligent information and database systems, ACIIDS 2009. IEEE, 465–470

  25. Zhang J, Wang Y (2008) A rough margin based support vector machine. Inf Sci 178(9):2204–2214

    Article  MathSciNet  Google Scholar 

  26. Lingras P, Butz CJ (2010) Rough support vector regression. Eur J Oper Res 206(2):445–455

    Article  Google Scholar 

  27. Zhao Y, Sun J (2009) Rough ν-support vector regression. Expert Syst Appl 36(6):9793–9798

    Article  Google Scholar 

  28. Xu Y, Wang L, Zhong P (2012) A rough margin-based ν-twin support vector machine. Neural Comput Appl 21(6):1307–1317

    Article  Google Scholar 

  29. Wang H, Zhou Z (2017) An improved rough margin-based ν-twin bounded support vector machine. Knowl-Based Syst 128:125–138

    Article  Google Scholar 

  30. Xu Y, Yu J, Zhang Y (2014) KNN-Based weighted rough ν-twin support vector machine. Knowl-Based Syst 71:303–313

    Article  Google Scholar 

  31. Karush W (2014) Minima of functions of several variables with inequalities as side conditions, Traces and Emergence of Nonlinear Programming. Springer Basel, pp 217–245

  32. Blake CL UCI repository of machine learning databases. http://archive.ics.uci.edu/ml/index.php

Download references

Acknowledgements

The authors wish to acknowledge the financial support of the National Nature Science Foundation of China (No.61562001), The China Scholarship Council Foundation (No.201408410287), The National Social Science Foundation of China (No.13BGL063) and High level Scientific research cultivation Foundation of Henan University of Science and Technology (No.2015GJB010).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471003, People’s Republic of China

    Zhenxia Xue

  2. Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI, 49855, USA

    Zhenxia Xue & Roxin Zhang

  3. School of Electrical and Computer Engineering, Oklahoma State University, Oklahoma, OK, 74054, USA

    Chuandong Qin

  4. School of Economics and management, Changsha University of Science and Technology, Changsha, 410004, People’s Republic of China

    Xiaoqing Zeng

Authors
  1. Zhenxia Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chuandong Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaoqing Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenxia Xue.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xue, Z., Zhang, R., Qin, C. et al. A rough ν-twin support vector regression machine. Appl Intell 48, 4023–4046 (2018). https://doi.org/10.1007/s10489-018-1185-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-018-1185-3

Keywords

Search

Navigation