Skip to main content
SpringerLink
Log in

Twin support vector regression for the simultaneous learning of a function and its derivatives

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Twin support vector regression (TSVR) determines a pair of \(\epsilon\)-insensitive up- and down-bound functions by solving two related support vector machine-type problems, each of which is smaller than that in a classical SVR. On the lines of TSVR, we have proposed a novel regressor for the simultaneous learning of a function and its derivatives, termed as TSVR of a Function and its Derivatives. Results over several functions of more than one variable demonstrate its effectiveness over other existing approaches in terms of improving the estimation accuracy and reducing run time complexity.

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. Antonio J, Martìn H, Santos M, Lope J (2010) Orthogonal variant moments features in image analysis. Inform Sci 180:846–860

    Article  MathSciNet  Google Scholar 

  2. Burges C (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Discov 2(2):121–167

    Article  Google Scholar 

  3. Beauchemin SS, Barron JL (1995) The computation of optical flow. ACM, New York

  4. Chen C, Zhang J, He X, Zhou Z (2011) Non-parametric Kernel learning with robust pairwise constraints. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0048-6

  5. Christianini N, Shawe-Taylor J (2000) An intorduction to support vector machines. Cambridge University Press, Cambridge

  6. Ebrahimi T, Garcia G, Vesin J (2002) Joint time-frequency-space classification of EEG in a brain–computer interface appplication. J Apply Signal Process 1:713–729

    Google Scholar 

  7. Fung G, Mangasarian OL (2001) Incremental support vector machine classification. In: 7th ACM SIGKDD international conference on knowledge discovery and data mining, pp 77–86

  8. Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The John Hopkins Univ. Press, Maryland

  9. He F, IAENG M, Yeung LM, Brown M (2008) Discrete-Time Model Representation for Biochemical Pathway Systems. IAENG Int J Comput Sci 34(1):1–15

    Google Scholar 

  10. Ince H, Trafalis TB (2000) Support vector machine for regression and applications to financial forecasting, In: International joint conference on neural networks, IJCNN, vol 6, pp 348–353

  11. Jayadeva, Khemchandani R, Chandra S (2006) Regularized least squares twin SVR for the simultaneous learning of a function and its derivative, IJCNN, pp 1192–1197

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

  13. Jayadeva, Khemchandani R, Chandra S (2008) Regularized least squares support vector regression for the simultaneous learning of a function and its derivatives. Inform Sci 178:3402–3414

  14. Joachims T (1999) Making large-scale SVM learning practical. In: Advances in kernel methods: support vector learning. MIT Press, Cambridge

  15. Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. In: Proceedings of the IEEE, pp 401–422

  16. Khemchandani R, Jayadeva, Chandra S (2009) Regularized least squares fuzzy support vector regression for financial time series forecasting. Exp Syst Appl 36:132–138

  17. Lagaris IE, Likas A, Fotiadis D (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9:987–1000

    Article  Google Scholar 

  18. Lengagne R (2000) 3D stereo reconstruction of human faces driven by differential constraints. Image Vis Comput 18:337-343

    Article  Google Scholar 

  19. Lázaro M, Santamaŕia I, Pérez-Cruz F, Artés-Rodŕiguez A (2005) Support vector regression for the simultaneous learning of a multivariate function and its derivative. Neurocomputing 69:42–61

    Article  Google Scholar 

  20. Lázaro M, Santamaria I, Pérez-Cruz F, Artés-Rodriguez A (2003) SVM for the simultaneous approximation of a function and its derivative. In: Proceedings of the 2003 IEEE international workshop on neural networks for signal processing (NNSP), Toulouse, France, pp 189–198

  21. Mangasarian OL (1998) Nonlinear programming. SIAM

  22. Liu Z, Wu Q, Zhang Y, Chen CLP (2011) Adaptive least squares support vector machines filter for hand tremor canceling in microsurgery. Int J Mach Learn Cybern 2(1):37–47

    Article  MathSciNet  Google Scholar 

  23. Mees AI, Jackson MF, Chua LO (1992) Device modeling by radial basis function. IEEE Trans Circuits Syst I Fundam Theory Appl 39:19–27

    Article  Google Scholar 

  24. Osuna E, Freund R, Girosi F (1997) Training support vector machines: an application to face detection. In: IEEE computer society conference on computer vision and pattern recognition, pp 130–136

  25. Peng X (2009) TSVR: an efficient twin support vector machine for regression. Neural Netw 23:365–372

    Article  Google Scholar 

  26. Pérez-Cruz F, Bousono-Calzón C, Artés-Rodriguez A (2005) Convergence of the IRWLS procedure to the support vector machine solution. Neural Comput 17:7–18

    Article  MATH  Google Scholar 

  27. Schmidt M, Lipson H (2009) Distilling free-form natural laws from experimental data. Science 324(5923):81–85

    Article  Google Scholar 

  28. Kemelmacher-Shlizerman I, Basri R (2011) 3D face reconstruction from a single image using a single reference face shape. IEEE Trans Pattern Anal Mach Intell 33(2):394–405

    Article  Google Scholar 

  29. Vapnik VN (1995) The nature of statistical learning theory. Springer, Berlin

  30. Vapnik VN (1998) Statistical learning theory. Wiley, NY

  31. Wang Z, Lu S, Zhai J (2008) Fast fuzzy multi-category SVM based on support vector domain description. Int J Pattern Recogn Artif Intell 22(1):109–120

    Article  Google Scholar 

  32. Xiao JZ, Wang HR, Yang X, Gao Z (2011) Multiple faults diagnosis in motion system based on SVM. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0035-y

  33. Zheng S (2011) Gradient descent algorithms for quantile regression with smooth approximation. Int J Mach Learn Cybern 2(3):191–207

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RBS India Development Centre, Gurgaon, Haryana, 122002, India

    Reshma Khemchandani

  2. Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, 110016, India

    Anuj Karpatne & Suresh Chandra

Authors
  1. Reshma Khemchandani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anuj Karpatne
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Suresh Chandra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reshma Khemchandani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khemchandani, R., Karpatne, A. & Chandra, S. Twin support vector regression for the simultaneous learning of a function and its derivatives. Int. J. Mach. Learn. & Cyber. 4, 51–63 (2013). https://doi.org/10.1007/s13042-012-0072-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-012-0072-1

Keywords

Search

Navigation