Polychotomous Machines;



Koo, Ja-Yong;Park, Heon Jin;Choi, Daewoo

  • 발행 : 2003.04.01


The support vector machine (SVM) is becoming increasingly popular in classification. The import vector machine (IVM) has been introduced for its advantages over SMV. This paper tries to improve the IVM. The proposed method, which is referred to as the polychotomous machine (PM), uses the Newton-Raphson method to find estimates of coefficients, and the Rao and Wald tests, respectively, for addition and deletion of import points. Because the PM basically follows the same addition step and adopts the deletion step, it uses, typically, less import vectors than the IVM without loosing accuracy. Simulated and real data sets are used to illustrate the performance of the proposed method.


classification;import vector;maximum likelihood;Newton-Raphson;reproducing kernel;stepwise algorithm


  1. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond Sch$"{o}$lkopt, B.;Smola, J.
  2. Statistical Learning Theory Vapnik, V.
  3. Learning Kernel Classifiers: Theroy and Algorithms Herbrich, R.
  4. Advances in Large Margin Classifiers Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods Platt, J.;Smola(ed.); Bartlett;Sch$\"{o}$lkopt(ed.);Schuurmans(ed.)
  5. Technical Report 1014. Department of Statistics Support Vector Machines and the Bayes rule in classification Lin, Y.
  6. Advances in Neural Information Processing Systems v.14 Kernel Logistic Regression and the Import Vector Machines Zhu, J.;Hastie, T.
  7. The Elements of Statistical Learning Hastie, T.;Tibshirani, R.;Friedman, J.
  8. Advances in Neural Information Processing Systems v.11 The Bias-Variance Tradeoff and the Randomized GACV Wahba, G.;Cohn(ed.);Kearns(ed.);Solla(ed.)
  9. Linear Statistical Inference and Its Applications(2nd edn.) Rao, C. R.