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Comparison of binary discrimination methods for high dimension low sample size data

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  • Bolivar-Cime, A.
  • Marron, J.S.

Abstract

A comparison of some binary discrimination methods is done in the high dimension low sample size context for Gaussian data with common diagonal covariance matrix. In particular we obtain results about the asymptotic behavior of the methods Support Vector Machine, Mean Difference (i.e. Centroid Rule), Distance Weighted Discrimination, Maximal Data Piling and Naive Bayes when the dimension d of the data sets tends to infinity and the sample sizes of the classes are fixed. It is concluded that, under appropriate conditions, the first four methods are asymptotically equivalent, but the Naive Bayes method can have a different asymptotic behavior when d tends to infinity.

Suggested Citation

  • Bolivar-Cime, A. & Marron, J.S., 2013. "Comparison of binary discrimination methods for high dimension low sample size data," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 108-121.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:108-121
    DOI: 10.1016/j.jmva.2012.10.001
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    References listed on IDEAS

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    1. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    2. Marron, J.S. & Todd, Michael J. & Ahn, Jeongyoun, 2007. "Distance-Weighted Discrimination," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1267-1271, December.
    3. Jeongyoun Ahn & J. S. Marron, 2010. "The maximal data piling direction for discrimination," Biometrika, Biometrika Trust, vol. 97(1), pages 254-259.
    4. Qiao, Xingye & Zhang, Hao Helen & Liu, Yufeng & Todd, Michael J. & Marron, J. S., 2010. "Weighted Distance Weighted Discrimination and Its Asymptotic Properties," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 401-414.
    5. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
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