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Training primal twin support vector regression via unconstrained convex minimization

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Abstract

In this paper, we propose a new unconstrained twin support vector regression model in the primal space (UPTSVR). With the addition of a regularization term in the formulation of the problem, the structural risk is minimized. The proposed formulation solves two smaller sized unconstrained minimization problems having continues, piece-wise quadratic objective functions by gradient based iterative methods. However, since their objective functions contain the non-smooth ‘plus’ function, two approaches are taken: (i) replace the non-smooth ‘plus’ function with their smooth approximate functions; (ii) apply a generalized derivative of the non-smooth ‘plus’ function. They lead to five algorithms whose pseudo-codes are also given. Experimental results obtained on a number of interesting synthetic and real-world benchmark datasets using these algorithms in comparison with the standard support vector regression (SVR) and twin SVR (TSVR) clearly demonstrates the effectiveness of the proposed method.

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References

  1. Balasundaram S, Gupta D (2014) Training Lagrangian twin support vector regression via unconstrained convex minimization. Knowl-Based Syst 59:85–96

    Article  MATH  Google Scholar 

  2. Balasundaram S, Gupta D (2013) On implicit Lagrangian twin support vector regression by Newton method. International Journal of Computational Intelligence Systems, pp 1–15

  3. Balasundaram S, Tanveer M (2013) On Lagrangian twin support vector regression. Neural Comput Appl 22(Suppl 1):S257– S267

    Article  Google Scholar 

  4. Box GEP, Jenkins GM (1976) Time series analysis: Forecasting and Control. Holden-Day, San Francisco

    MATH  Google Scholar 

  5. Brown MPS, Grundy WN, Lin D et al (2000) Knowledge-based analysis of microarray gene expression data using support vector machine. Proc Nat Acad Sci USA 97(1):262–267

    Article  Google Scholar 

  6. Chapelle O (2007) Training a support vector machine in primal. Neural Comput 19(5):1155–1178

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen X, Yang J, Liang J, Ye Q (2012) Smooth twin support vector regression. Neural Comput Appl 21:505–513

    Article  Google Scholar 

  8. Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel based learning method. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  9. Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  MATH  Google Scholar 

  10. Eubank RL (1999) Nonparametric regression and spline smoothing statistics: Textbooks and monographs, vol 157, 2nd edn. NY, Marcel Dekker

  11. Fung G, Mangasarian OL (2003) Finite Newton method for Lagrangian support vector machine. Neurocomputing 55:39–55

    Article  Google Scholar 

  12. Garcia S, Herrera F (2008) An extension on “Statistical comparisons of classifiers over multiple data sets” for all pairwise comparisons. J Mach Learn Res 9:2677–2694

    MATH  Google Scholar 

  13. Gretton A, Doucet A, Herbrich R, Rayner PJW, Scholkopf B (2001) Support vector regression for black-box system identification. In: Proceedings of the 11 th IEEE Workshop on Statistical Signal Processing

  14. Guyon I, Weston J, Barnhill S, Vapnik V (2002) Gene selection for cancer classification using support vector machine. Mach Learn 46:389–422

    Article  MATH  Google Scholar 

  15. Hiriart-Urruty J-B, Strodiot JJ, Nguyen VH (1984) Generalized hessian matrix and second-order optimality conditions for problems with C L1 data. Appl Math Opt 11:43–56

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  17. Joachims T, Ndellec C, Rouveriol (1998) Text categorization with support vector machines: learning with many relevant features. In: European Conference on Machine Learning No. 10. Chemnitz, Germany, pp 137–142

  18. Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recogn Lett 29:1842–1848

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Lee YJ, Mangasarian OL (2001) SSVM: A smooth support vector machine for classification. Comput Opt Appl 20(1):5–22

    Article  MathSciNet  MATH  Google Scholar 

  21. Lee YJ, Hsieh W-F, Huang C-M (2005) ε-SSVR: A smooth support vector machine for ε-insensitive regression. IEEE Trans Knowl Data Eng 17(5):678–685

    Article  Google Scholar 

  22. Mangasarian OL (2002) A finite Newton method for classification. Opt Methods Softw 17:913–929

    Article  MathSciNet  MATH  Google Scholar 

  23. Mangasarian OL, Musicant DR (2001) Lagrangian support vector machines. J Mach Learn Res 1:161–177

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  25. Mukherjee S, Osuna E, Girosi F (1997) Nonlinear prediction of chaotic time series using support vector machines. In: NNSP’97: Neural Networks for Signal Processing VII: in Proceedings of IEEE Signal Processing Society Workshop, Amelia Island, FL, USA, pp 511–520

  26. Muller KR, Smola AJ, Ratsch G, Schölkopf B, Kohlmorgen J (1999) Using support vector machines for time series prediction. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in Kernel Methods- Support Vector Learning. MIT Press, Cambridge, MA, pp 243–254

  27. Murphy PM, Aha DW (1992) UCI repository of machine learning databases. University of California, Irvine. http://www.ics.uci.edu/~mlearn

  28. Osuna E, Freund R, Girosi F (1997) Training support vector machines: An application to face detection. In: Proceedings of Computer Vision and Pattern Recognition, 130-136

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

    Article  Google Scholar 

  30. Peng X (2010) Primal twin support vector regression and its sparse approximation. Neurocomputing 73 (16-18):2846–2858

    Article  Google Scholar 

  31. Peng X (2012) Efficient twin parametric insensitive support vector regression model. Neurocomputing 79:26–38

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Shao Y, Zhang C, Yang Z, Jing L, Deng N (2012) An ε− twin support vector machine for regression. Neural Comput Appl. doi:10.1007/s00521-012-00924-3

    Google Scholar 

  34. Sjoberg J, Zhang Q, Ljung L, Berveniste A, Delyon B, Glorennec P, Hjalmarsson H, Juditsky (1995) Nonlinear black-box modeling in system identification: a unified overview. Automatica 31:1691–1724

    Article  MathSciNet  MATH  Google Scholar 

  35. Souza LGM, Barreto GA (2006) Nonlinear system identification using local ARX models based on the self-organizing map. In: Learning and Nonlinear Models-Revista da Soc Brasileira de Redes Neurals (SBRN), vol 4, no 2, pp 112–123

  36. Van Gestel T, Baesens B, Suykens JAK, De Espinoza M, Baestaens J, Vanthienen De MB (2003) Bankruptcy prediction with least squares support vector machine classifiers. In: Proceedings IEEE Int conf computational intelligence for financial engineering, Hong Kong

  37. Vapnik VN (2000) The nature of statistical learning theory, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  38. Wang XX, Chen S, Lowe D, Harris CJ (2006) Sparse support vector regression based on orthogonal forward selection for generalized kernel model. Neurocomputing 70:462–474

    Article  Google Scholar 

  39. Xu Y, Wang L (2012) A weighted twin support vector regression. Knowl Based Syst 33:92–101

    Article  Google Scholar 

  40. Yang X, Zhang G, Lu J, Ma J (2011) A kernel fuzzy c-means clustering-based fuzzy support vector machine algorithm for classification problems with outliers or noises. IEEE Trans Fuzzy Syst 19(1):105–115

    Article  Google Scholar 

  41. Zhong P, Xu Y, Zhao Y (2012) Training twin support vector regression via linear programming. Neural Comput Appl 21:399–407

    Article  Google Scholar 

  42. Zhao Y, Zhao J, Zhao M (2013) Twin least squares support vector regression. Neurocomputing 118:225–236

    Article  Google Scholar 

Download references

Acknowledgments

The authors are extremely thankful to the anonymous reviewers for their comments. Mr.Yogendra Meena acknowledges the financial assistance awarded by Rajiv Gandhi National Fellowship, Government of India.

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Authors and Affiliations

  1. School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi, 110067, India

    S. Balasundaram & Yogendra Meena

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  1. S. Balasundaram
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  2. Yogendra Meena
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Correspondence to S. Balasundaram.

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Balasundaram, S., Meena, Y. Training primal twin support vector regression via unconstrained convex minimization. Appl Intell 44, 931–955 (2016). https://doi.org/10.1007/s10489-015-0731-5

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