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Improving the Generalization Error Bound using Total margin in Support Vector Machines

서포트 벡터 기계에서 TOTAL MARGIN을 이용한 일반화 오차 경계의 개선

  • Yoon, Min (Dept. of Applied Statistics, Yonsei University)
  • 윤민 (연세대학교 응용통계학과)
  • Published : 2004.03.01

Abstract

The Support Vector Machine(SVM) algorithm has paid attention on maximizing the shortest distance between sample points and discrimination hyperplane. This paper suggests the total margin algorithm which considers the distance between all data points and the separating hyperplane. The method extends existing support vector machine algorithm. In addition, this newly proposed method improves the generalization error bound. Numerical experiments show that the total margin algorithm provides good performance, comparing with the previous methods.

서포트 벡터 기계(Support Vector Machines, SVMs) 알고리즘은 표본 점들과 분리 초평면 사이의 최소 거리를 최대화하는 것에 관심을 가져왔다. 본 논문은 모든 데이터 점들과 분리 초평면 사이의 거리들을 고려하는 total margin을 제안한다. 본 논문에서 제안하는 방법은 기존의 서포트 벡터 기계 알고리즘을 확장하고, 일반화 오차 경계를 개선하게 된다. 새롭게 제안하는 total margin알고리즘이 기존 방법들과의 비교를 통하여 더욱 우수한 수행능력을 가지고 있음을 수치 예제들을 통하여 확인할 수 있다.

Keywords

References

  1. 응용통계연구 v.16 no.2 서포트 벡터 기계에서 잡음 영향의 효과적 조절 김철응;윤민 https://doi.org/10.5351/KJAS.2003.16.2.261
  2. Journal of ACM v.44 Scale-Sensitive Dimensions, Uniform Convergence, and Learnability. Alon, N.;Ben-David, S.;Cesa-Bianchi, N.;Hasssler, D. https://doi.org/10.1145/263867.263927
  3. Advances in Kernel Method-Support Vector learning Generalization Performance of Support Vector Machines an Other Pattern Classifiers. Bartlett, P.;Shawe-Taylor, J.;Scholkopf, B(ed.);Burges, C. J. C(ed.);Smola, A(ed.).
  4. Nonlinear Programming Bertsekas, D. P.
  5. Learning from Data Concept, Theory, and Methods Cherkassky, V.;Mulier, F.
  6. Ph.D.Thesis, University of Rochester Prediction of Generalization Ability in Learning Systems Cortes, C.
  7. An Introduction to Support Vector Machines and other kernel-based learning methods Cristianini, N.;Shawe-Taylor, J.
  8. Machine Learning: Proceedings of the 15th International Conference Large margin classification using the preceptron algorithm Freund, Y.;Schapire, R. E.;Shavlik, J(ed.).
  9. European Journal of Operational Research v.7 Simple but Powerful Goal Programming Model for Discriminant Problems Freed, N.;Glover, F. https://doi.org/10.1016/0377-2217(81)90048-5
  10. Proceedings of Algorithmic Theory, ALT-97 A Note on a Scale-Sensitive Dimension of Linear Bounded Functionals in Banach Spaces Gurvits, L.
  11. Neural Networks A Comprehensive Foundation(2nd ed.) Haykin, S.
  12. Advances in Large Margin Classifiers Mangasarian, O. L.;Smola, A(ed.);Bartlett, B(ed.);Scholkopf, B(ed.);Schuurmans, D(ed.)
  13. Annlas Statistics v.26 Boosting the Margin: A New Explanation for the Effectiveness of Voting methods Schapire, R.;Freund, Bartlett, Y. P.;Sun Lee, W. https://doi.org/10.1214/aos/1024691352
  14. IEEE Transactions on Information Theory v.44 Structural Risk Minimization over Data-Dependent Hierarchies Shawe-Taylor, J.;Bartlett, P.L.;Williamson, R.C.;Anthony, M. https://doi.org/10.1109/18.705570
  15. NeuroCOLT2 Technical Report Series, NC-TR-2000-082 On the generalization of Soft margin Algorithms Shawe-Taylor, J.;Cristianini, N.
  16. NeuroCOLT2 Technical Report, NeuroCOLT A Tutorial on Support Vector Regression Smola, A.J.;Scholkopf, B.
  17. The Nature of Statistical Learning Theory(2nd ed.) Vapnik, V.