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Classification Based on the Support Vector Machine and on Regression Depth

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Statistical Data Analysis Based on the L1-Norm and Related Methods

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

This paper compares modern classification methods based on the support vector machine (SVM) and on the regression depth method (RDM) with classical linear and quadratic discriminant analysis.

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References

  1. A. Albert and J.A. Anderson. On the existence of maximum likelihood estimates in logistic regression models. Biometrika 71 (1984), 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Christmann, P. Fischer, and T. Joachims. Comparison between the regression depth method and the support vector machine to approximate the minimum number of misclassifications. To appear in: Computational Statistics (2002).

    Google Scholar 

  3. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Data Mining, Inference, and Prediction. Springer, 2001.

    Google Scholar 

  4. K.U. Höffgen, H.U. Simon, and K.S. van Horn. Robust Trainability of Single Neurons. J. Computer and System Sciences 50 (1995), 114–125.

    Article  MATH  Google Scholar 

  5. T. Joachims. Making large-Scale SVM Learning Practical. In: B. Schölkopf, C. Burges, A. Smola (ed.), Advances in Kernel Methods — Support Vector Learning, MIT-Press, 1999. http://www-ai.cs.uni-dortmund.de/svm_light

    Google Scholar 

  6. D. Meyer. Support Vector Machines. The Interface to libsvm in package e1071. Online-Documentation of the package e1071 for “R”.

    Google Scholar 

  7. A. Novikoff. On convergence proofs on perceptrons. Proceedings of the Symposium on the Mathematical Theory of Automata, Vol XII, 615–622.

    Google Scholar 

  8. F. Rosenblatt. Principles of Neurodynamics. Spartan. New York, 1962.

    MATH  Google Scholar 

  9. Rousseeuw, P.J. and Hubert, M. (1999). Regression Depth. J. Amer. Statist Assoc., 94, 388–433.

    Article  MATH  MathSciNet  Google Scholar 

  10. P.J. Rousseeuw, and A. Struyf. Computing location depth and regression depth in higher dimensions. Statistics and Computing 8 (1998), 193–203.

    Article  Google Scholar 

  11. T.J. Santner and D.E. Duffy. A note on A. Albert and J.A. Anderson’s conditions for the existence of maximum likelihood estimates in logistic regression models. Biometrika 73 (1986), 755–758.

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Schölkopf and A.J. Smola. Learning with Kernels. Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, 2002.

    Google Scholar 

  13. V. Vapnik, Statistical Learning Theory. Wiley, 1998.

    Google Scholar 

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Author information

Authors and Affiliations

  1. HRZ, University of Dortmund, D-44221, Dortmund, Germany

    Andreas Christmann

Authors
  1. Andreas Christmann
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Editor information

Editors and Affiliations

  1. Statistics Group, University of Neuchâtel, P.O. Box 805, CH-2002, Neuchâtel, Switzerland

    Yadolah Dodge (Prof. of Statistics and Operation Research) (Prof. of Statistics and Operation Research)

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© 2002 Springer Basel AG

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Christmann, A. (2002). Classification Based on the Support Vector Machine and on Regression Depth. In: Dodge, Y. (eds) Statistical Data Analysis Based on the L1-Norm and Related Methods. Statistics for Industry and Technology. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8201-9_28

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  • DOI: https://doi.org/10.1007/978-3-0348-8201-9_28

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9472-2

  • Online ISBN: 978-3-0348-8201-9

  • eBook Packages: Springer Book Archive

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