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Article

Asymptotic properties of multiclass support vector machine under high dimensional settings

Pages 1991-2005 | Received 19 Nov 2021, Accepted 08 Apr 2022, Published online: 26 Apr 2022

References

  • Aoshima, M., and K. Yata. 2011. Two-stage procedures for high-dimensional data. Sequential Analysis (Editor’s Special Invited Paper 30 (4):356–99. doi:10.1080/07474946.2011.619088.
  • Aoshima, M., and K. Yata. 2014. A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data. Annals of the Institute of Statistical Mathematics 66 (5):983–1010. doi:10.1007/s10463-013-0435-8.
  • Aoshima, M., and K. Yata. 2015. Geometric classifier for multiclass, high-dimensional data. Sequential Analysis 34 (3):279–94. doi:10.1080/07474946.2015.1063256.
  • Aoshima, M., and K. Yata. 2019a. Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models. Annals of the Institute of Statistical Mathematics 71 (3):473–503. doi:10.1007/s10463-018-0655-z.
  • Aoshima, M., and K. Yata. 2019b. High-dimensional quadratic classifiers in non-sparse settings. Methodology and Computing in Applied Probability 21 (3):663–82. doi:10.1007/s11009-018-9646-z.
  • Chan, Y.-B., and P. Hall. 2009. Scale adjustments for classifiers in high-dimensional, low sample size settings. Biometrika 96 (2):469–78. doi:10.1093/biomet/asp007.
  • Egashira, K., K. Yata, and M. Aoshima. 2021. Asymptotic properties of distance weighted discrimination and its bias correction for high-dimension, low-sample-size data. Japanese Journal of Statistics and Data Science 4 (2):821–40. doi:10.1007/s42081-021-00135-x.
  • Hall, P., J. S. Marron, and A. Neeman. 2005. Geometric representation of high dimension, low sample size data. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67 (3):427–44. doi:10.1111/j.1467-9868.2005.00510.x.
  • Hall, P., Y. Pittelkow, and M. Ghosh. 2008. Theoretical measures of relative performance of classifiers for high dimensional data with small sample sizes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70 (1):159–73. doi:10.1111/j.1467-9868.2007.00631.x.
  • Huang, H., Y. Liu, Y. Du, C. M. Perou, D. N. Hayes, M. J. Todd, and J. S. Marron. 2013. Multiclass distance-weighted discrimination. Journal of Computational and Graphical Statistics 22 (4):953–69. doi:10.1080/10618600.2012.700878.
  • Khan, J., J. S. Wei, M. Ringner, L. H. Saal, M. Ladanyi, F. Westermann, F. Berthold, M. Schwab, C. R. Antonescu, C. Peterson, et al. 2001. Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks. Nature Medicine 7 (6):673–9. doi:10.1038/89044.
  • Lee, Y., Y. Lin, and G. Wahba. 2004. 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):67–82. doi:10.1198/016214504000000098.
  • Marron, J. S., M. J. Todd, and J. Ahn. 2007. Distance-weighted discrimination. Journal of the American Statistical Association 102 (480):1267–71. doi:10.1198/016214507000001120.
  • Nakayama, Y., K. Yata, and M. Aoshima. 2017. Support vector machine and its bias correction in high-dimension, low-sample-size settings. Journal of Statistical Planning and Inference 191:88–100. doi:10.1016/j.jspi.2017.05.005.
  • Nakayama, Y., K. Yata, and M. Aoshima. 2020. Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings. Annals of the Institute of Statistical Mathematics 72 (5):1257–86. doi:10.1007/s10463-019-00727-1.
  • Qiao, X., and L. Zhang. 2015. Flexible high-dimensional classification machines and their asymptotic properties. Journal of Machine Learning Research 16:1547–72.
  • Qiao, X., H. H. Zhang, Y. Liu, M. J. Todd, and J. S. Marron. 2010. Weighted distance weighted discrimination and its asymptotic properties. Journal of the American Statistical Association 105 (489):401–14. doi:10.1198/jasa.2010.tm08487.
  • Vapnik, V. N. 2000. The nature of statistical learning theory. 2nd ed. New York: Springer.

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