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DC programming and DCA for parametric-margin ν-support vector machine

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Abstract

As a development of ν-support vector machine (ν-SVM), parametric-margin ν-support vector machine (Par-ν-SVM) can be useful in many cases, especially heteroscedastic noise classification problems. The present article proposes a novel and fast method to solve the primal problem of Par-ν-SVM (named as DC-Par-ν-SVM), while Par-ν-SVM maximizes the parametric-margin by solving a dual quadratic programming problem. In fact, the primal non-convex problem is converted into an unconstrained problem to express the objective function as the difference of convex functions (DC). The DC-Algorithm (DCA) based on generalized Newton’s method is proposed to solve the unconstrained problem cited. Numerical experiments performed on several artificial, real-life, UCI and NDC data sets showed the superiority of the DC-Par-ν-SVM in terms of both accuracy and learning speed.

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References

  1. Angulo C, Parra X, Catala A (2003) K-SVCR. A support vector machine for multi-class classification. Neurocomputing 55(1-2):57–77

    Article  Google Scholar 

  2. Artacho FJA, Fleming RM, Vuong PT (2018) Accelerating the DC algorithm for smooth functions. Math Program 169(1):95–118

    Article  MathSciNet  MATH  Google Scholar 

  3. Amin M, Ali A (2018) Performance evaluation of supervised machine learning classifiers for predicting healthcare operational decisions. Wavy AI Research Foundation, Lahore

    Google Scholar 

  4. Ayres-de-Campos D, Bernardes J, Garrido A, Marques-de-Sa J, Pereira-Leite L (2000) SisPorto 2.0: a program for automated analysis of cardiotocograms. Journal of Maternal-Fetal Medicine 9(5):311–318

    Google Scholar 

  5. Bennett KP, Bredensteiner EJ (2000) Duality and geometry in SVM classifiers. In: ICML, pp 57–64

  6. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  7. Bradley PS, Mangasarian OL (2000) Massive data discrimination via linear support vector machines. Optimization methods and software 13(1):1–10

    Article  MathSciNet  MATH  Google Scholar 

  8. Burges CJ (1998) A tutorial on support vector machines for pattern recognition. Data mining and knowledge discovery 2(2):121–167

    Article  Google Scholar 

  9. Belghiti MT, Tao PD (2007) A new efficient algorithm based on DC programming and DCA for clustering. J Glob Optim 37(4):593–608

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen X, Yang J, Liang J (2012) A flexible support vector machine for regression. Neural Comput Appl 21(8):2005–2013

    Article  Google Scholar 

  11. Cherkassky V, Mulier FM (2007) Learning from data: Concepts, theory, and methods. Wiley, New York

    Book  MATH  Google Scholar 

  12. Clarke FH (1990) Optimization and nonsmooth analysis, Siam

  13. Daniel WW (1990) Friedman two-way analysis of variance by ranks, Applied nonparametric statistics, 262–274

  14. Ding S, An Y, Zhang X, Wu F, Xue Y (2017) Wavelet twin support vector machines based on glowworm swarm optimization. Neurocomputing 225:157–163

    Article  Google Scholar 

  15. Friedman M (1940) A comparison of alternative tests of significance for the problem of m rankings. The Annals of Mathematical Statistics 11(1):86–92

    Article  MathSciNet  MATH  Google Scholar 

  16. Hao PY (2010) New support vector algorithms with parametric insensitive/margin model. Neural Netw 23 (1):60–73

    Article  MATH  Google Scholar 

  17. Hiriart-Urruty JB, Strodiot JJ, Nguyen VH (1984) Generalized Hessian matrix and second-order optimality conditions for problems with C 1,1 data. Appl Math Optim 11(1):43–56

    Article  MathSciNet  MATH  Google Scholar 

  18. Horst R, Pardalos PM, Van Thoai N (2000) Introduction to global optimization, Springer Science & Business Media

  19. Hong ZQ, Yang JY (1991) Optimal discriminant plane for a small number of samples and design method of classifier on the plane. Pattern Recogn 24(4):317–324

    Article  MathSciNet  Google Scholar 

  20. Iman RL, Davenport JM (1980) Approximations of the critical region of the fbietkan statistic. Communications in Statistics-Theory and Methods 9(6):571–595

    Article  MATH  Google Scholar 

  21. Karasuyama M, Harada N, Sugiyama M, Takeuchi I (2012) Multi-parametric solution-path algorithm for instance-weighted support vector machines. Mach Learn 88(3):297–330

    Article  MathSciNet  MATH  Google Scholar 

  22. Ketabchi S, Moosaei H, Razzaghi M, Pardalos PM (2019) An improvement on parametric ν-support vector algorithm for classification. Ann Oper Res 276(1-2):155–168

    Article  MathSciNet  MATH  Google Scholar 

  23. Ketabchi S, Moosaei H (2012) Minimum norm solution to the absolute value equation in the convex case. J Optim Theory Appl 154(3):1080–1087

    Article  MathSciNet  MATH  Google Scholar 

  24. Khozeimeh F, Alizadehsani R, Roshanzamir M, Khosravi A, Layegh P, Nahavandi S (2017) An expert system for selecting wart treatment method. Comput Bio Med 81:167–175

    Article  Google Scholar 

  25. Khozeimeh F, Jabbari Azad F, Mahboubi Oskouei Y, Jafari M, Tehranian S, Alizadehsani R, Layegh P (2017) Intralesional immunotherapy compared to cryotherapy in the treatment of warts. Int J Dermatology 56 (4):474–478

    Article  Google Scholar 

  26. Koczkodaj WW, Kakiashvili T, Szymanska A, Montero-Marin J, Araya R, Garcia-Campayo J, Rutkowski K, Strzalka D (2017) How to reduce the number of rating scale items without predictability loss. Scientometrics 111(2):581–593

    Article  Google Scholar 

  27. Le Thi HA, Dinh TP, Yen ND (2011) Properties of two DC algorithms in quadratic programming. J Glob Optim 49(3):481–495

    Article  MathSciNet  MATH  Google Scholar 

  28. Le Thi HA, Dinh TP (2018) DC programming and DCA: thirty years of developments. Math Program 169(1):5–68

    Article  MathSciNet  MATH  Google Scholar 

  29. Lichman M (2013) UCI machine learning repository. University of California, School of Information and Computer Science , Irvine

    Google Scholar 

  30. Lima MD, Costa NL, Barbosa R (2018) Improvements on least squares twin multi-class classification support vector machine. Neurocomputing 313:196–205

    Article  Google Scholar 

  31. Mayoraz E, Alpaydin E (1999) Support vector machines for multi-class classification. In: International work-conference on artificial neural networks. Springer, Berlin

  32. Melki G, Kecman V, Ventura S, Cano A (2018) OLLAWV:online learning algorithm using worst-violators. Appl Soft Comput 66:384–393

    Article  Google Scholar 

  33. Musicant DR (1998) NDC: Normally distributed clustered data sets. Computer Sciences Department, University of Wisconsin

    Google Scholar 

  34. Pardalos PM, Ketabchi S, Moosaei H (2014) Minimum norm solution to the positive semidefinite linear complementarity problem. Optimization 63(3):359–369

    Article  MathSciNet  MATH  Google Scholar 

  35. Patricio M, Pereira J, Crisostomo J, Matafome P, Gomes M, Seica R, Caramelo F (2018) Using Resistin, glucose, age and BMI to predict the presence of breast cancer. BMC Cancer 18 (1):29

    Article  Google Scholar 

  36. Peng X (2011) TPMSVM: A novel twin parametric-margin support vector machine for pattern recognition. Pattern Recogn 44(10-11):2678–2692

    Article  MATH  Google Scholar 

  37. Schölkopf B, Smola AJ, Bach F (2002) Learning with kernels:support vector machines, regularization, optimization, and beyond. MIT Press, Cambridge

    Google Scholar 

  38. Schölkopf B, Smola AJ, Williamson RC, Bartlett PL (2000) New support vector algorithms. Neural Comput 12(5):1207–1245

    Article  Google Scholar 

  39. Tanveer M, Khan MA, Ho SS (2016) Robust energy-based least squares twin support vector machines. Appl Intell 45(1):174– 186

    Article  Google Scholar 

  40. Tao PD, Muu LD (1996) Numerical solution for optimization over the efficient set by dc optimization algorithms. Oper Res Lett 19(3):117–128

    Article  MathSciNet  MATH  Google Scholar 

  41. Vapnik V, Chervonenkis A (1974) Theory of pattern recognition. Nauka, Moscow. [in Russian]

    MATH  Google Scholar 

  42. Vapnik V (2013) The nature of statistical learning theory, Springer science & business media

  43. Wang H, Zhou Z, Xu Y (2018) An improved ν-twin bounded support vector machine. Appl Intell 48(4):1041–1053

    Article  Google Scholar 

  44. Xu Y (2016) K-nearest neighbor-based weighted multi-class twin support vector machine. Neurocomputing 205:430–438

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Fatemeh Bazikar & Saeed Ketabchi

  2. Department of Mathematics, Faculty of Science, University of Bojnord, Bojnord, Iran

    Hossein Moosaei

Authors
  1. Fatemeh Bazikar
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  2. Saeed Ketabchi
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  3. Hossein Moosaei
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Correspondence to Saeed Ketabchi.

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Bazikar, F., Ketabchi, S. & Moosaei, H. DC programming and DCA for parametric-margin ν-support vector machine. Appl Intell 50, 1763–1774 (2020). https://doi.org/10.1007/s10489-019-01618-x

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