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Estimation of the Misclassification Error for Multicategory Support Vector Machine Classification 被引量：3

Estimation of the Misclassification Error for Multicategory Support Vector Machine Classification
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摘要 The purpose of this paper is to provide an error analysis for the multicategory support vector machine （MSVM） classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results. The purpose of this paper is to provide an error analysis for the multicategory support vector machine （MSVM） classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results.
作者 Bing Zheng LI
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第3期511-528,共18页 数学学报（英文版）
关键词 multicategory support vector machine CLASSIFIER misclassification error reproducing kernel Hilbert space approximation error multicategory, support vector machine, classifier, misclassification error, reproducing kernel Hilbert space, approximation error
分类号 O15 [理学—基础数学]
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参考文献21

  • 1Wu, Q., Zhou, D. X.: Analysis of support vector machine classificaton. J. Comp. Anal. Appl., 8, 99-119 (2006)
  • 2Chen, D. R., Wu, Q., Ying, Y., Zhou, D. X.: Support vector machine soft margin classifier: error analysis. J. Machine Learning Research, 5, 1143-1175 (2004)
  • 3Dietterich, T. G., Bakiri, G.: Soving multiclass learning problems via error-correcting output codes. Journal of Articficial Intelligence Rearch, 2, 263-286 (1995)
  • 4Lee, Y., Lin, Y., Wahba, G.: Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data. Journal of the American Statistical Association, 99(465), 67-81 (2004)
  • 5Strauss, D. J., Stcidl, G.: Hybrid wavelet-support vection classification of waveforms. J. Comp. and Appl. Math., 148, 375-400 (2002)
  • 6Lin, Y.: Support Vector Machines and the Bayes Rule in classification. Data Mining and Knowledge Discovery, 6, 259-275 (2002)
  • 7Smale, S.Zhou, D. X.: Estimating the approximation error in learning theory. Anal. App., 1, 17-41 (2003)
  • 8Cristianini, N., Shawe-Taylor, J.: An introduction to support vector machines, Cambridge University Press, Cambridge, 2000
  • 9Steinwart, I.: Support vector machines are universally consistent. J. Complexity, 18, 768-791, 21-49 (2002) .
  • 10Vapnik, V.: Statistical Learning Theory, John Wiley & Sons, 1998

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Acta Mathematica Sinica,English Series
2008年 第3期

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