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Robust multiclass kernel-based classifiers

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Abstract

In this research, a robust optimization approach applied to multiclass support vector machines (SVMs) is investigated. Two new kernel based-methods are developed to address data with input uncertainty where each data point is inside a sphere of uncertainty. The models are called robust SVM and robust feasibility approach model (Robust-FA) respectively. The two models are compared in terms of robustness and generalization error. The models are compared to robust Minimax Probability Machine (MPM) in terms of generalization behavior for several data sets. It is shown that the Robust-SVM performs better than robust MPM.

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References

  1. Bennett, K., Mangasarian, O.: Robust linear programming discrimination of two linearly inseparable sets. Optim. Methods Softw. 1, 23–34 (1992)

    Article  Google Scholar 

  2. Ben-Tal, A., Nemirovski, A.: Robust solutions to uncertain linear program via convex programming. Oper. Res. Lett. 25(1), 1–17 (1996)

    Article  MathSciNet  Google Scholar 

  3. Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23(4), 769–805 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bertsimas, D., Pachamanova, D., Sim, M.: Robust linear optimization under general norms, Oper. Res. Lett. (April), 510–516 (2004)

  5. Birge, J.: The value of statistic solution in stochastic linear programming with fixed resources. Math. Program. 24, 314–325 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  6. Blake, C., Merz, C.: UCI Repository of machine learning databases. http://www.ics.uci.edu/~mlearn/MLRepository.html (1998)

  7. Boyd, S., Lobo, M., Vandenberghe, L.: Application of second-order cone programming. Linear Algebra Appl. 284, 193–226 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chvatal, V.: Linear Programming. Freeman, New York (1983)

    MATH  Google Scholar 

  9. Fung, G.M., Mangasarian, O., Shavlik, J.: Knowledge-based support vector machines classifiers. Technical report 01-09, Data Mining Institute, Computer Sciences Department, University of Wisconsin (2001)

  10. Ghaoui, L.E., Lanckriet, G., Natsoulis, G.: Robust classification with interval data. Technical report CSD-03-1279, Division of Computer Science, University of California, Berkeley (2003) http://robotics.eecs.berkeley.edu/~gert/

  11. Ghaoui, L.E., Lebret, H.: Robust solutions to least square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035–1064 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ghaoui, L.E., Oustry, F., Lebret, H.: Robust solutions to uncertain semidefinite programs. SIAM J. Optim. 18, 1035–1064 (1997)

    MATH  Google Scholar 

  13. Gill, P., Murray, W., Saunders, M.: Snopt: An SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12(4), 979–1006 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York (2001)

    MATH  Google Scholar 

  15. Haykin, S.: Neural Network: a Comprehensive Foundation. Prentice-Hall, New Jersey (1999)

    MATH  Google Scholar 

  16. Hsu, C.-W., Lin, C.-J.: A comparison of methods for multi-class support vector machines. IEEE Trans. Neural Networks 13, 415–425 (2002)

    Article  Google Scholar 

  17. Lanckriet, G., Ghaoui, L.E., Bhattacharyya, C., Jordan, M.: A robust minimax approach to classification. J. Mach. Learn. Res. 3, 555–582 (2002)

    Article  Google Scholar 

  18. Popescue, I., Bertsimas, D.: Optimal inequalities in probability theory: a convex optimization approach, Technical report TM62, INSEAD (2001)

  19. Schölkopf, B., Smola, A.: Learning with Kernels. MIT, Cambridge (2002)

    Google Scholar 

  20. Street, W., Mangasarian, O.: Improved generalization error via tolerant training. J. Optim. Theory Appl. 96(2), 259–279 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  21. Trafalis, T., Alwazzi, S.: Robust optimization in support vector machine training with bounded errors. In: Proceedings of the International Joint Conference on Neural Networks, Portland, OR, pp. 2039–2042. IEEE, New York (2003)

    Chapter  Google Scholar 

  22. Trafalis, T., Alwazzi, S.: Robust support vector regression and applications. In: Dagli, C., Buczak, A., Ghosh, J., Embrechts, M., Ersoy, O., Kerc, S. (eds.) Intelligent Engineering Systems through Artificial Neural Networks, vol. 13, pp. 181–186. ASME, New York (2003)

    Google Scholar 

  23. Trafalis, T.B., Oladunni, O., Papavassiliou, D.V.: Two-phase flow regime identification with a multi-classification SVM model. Ind. Eng. Chem. Res. 44, 4414–4426 (2005)

    Article  Google Scholar 

  24. Trafalis, T., Santosa, B., Richman, M.: Tornado detection with kernel-based methods. In: Dagli, C., Buczak, A., Ghosh, J., Embrechts, M., Ersoy, O., Kerc, S. (eds.) Intelligent Engineering Systems through Artificial Neural Networks 13, pp. 677–682. ASME, New York (2003)

    Google Scholar 

  25. Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)

    MATH  Google Scholar 

  26. Weston, J., Watkins, C.: Support vector machines for multi-class pattern recognition. In: Proceeding of the Seventh European Symposium on Artificial Neural Networks, pp. 219–224 (1999)

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Authors and Affiliations

  1. Department of Industrial Engineering, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia

    Budi Santosa

  2. School of Industrial Engineering, University of Oklahoma, Norman, USA

    Theodore B. Trafalis

Authors
  1. Budi Santosa
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  2. Theodore B. Trafalis
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Correspondence to Theodore B. Trafalis.

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Santosa, B., Trafalis, T.B. Robust multiclass kernel-based classifiers. Comput Optim Appl 38, 261–279 (2007). https://doi.org/10.1007/s10589-007-9042-z

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