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Sparse HDLSS discrimination with constrained data piling

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  • Ahn, Jeongyoun
  • Jeon, Yongho

Abstract

Regularization is a key component in high dimensional data analyses. In high dimensional discrimination with binary classes, the phenomenon of data piling occurs when the projection of data onto a discriminant vector is dichotomous, one for each class. Regularizing the degree of data piling yields a new class of discrimination rules for high dimension–low sample size data. A discrimination method that regularizes the degree of data piling while achieving sparsity is proposed and solved via a linear programming. Computational efficiency is further improved by a sign-preserving regularization that forces the signs of the estimator to be the same as the mean difference. The proposed classifier shows competitive performances for simulated and real data examples including speech recognition and gene expressions.

Suggested Citation

  • Ahn, Jeongyoun & Jeon, Yongho, 2015. "Sparse HDLSS discrimination with constrained data piling," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 74-83.
    • Handle: RePEc:eee:csdana:v:90:y:2015:i:c:p:74-83
    DOI: 10.1016/j.csda.2015.04.006
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    References listed on IDEAS

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    1. Jeongyoun Ahn & J. S. Marron, 2010. "The maximal data piling direction for discrimination," Biometrika, Biometrika Trust, vol. 97(1), pages 254-259.
    2. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    3. Trendafilov, Nickolay T. & Jolliffe, Ian T., 2007. "DALASS: Variable selection in discriminant analysis via the LASSO," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3718-3736, May.
    4. Qing Mai & Hui Zou & Ming Yuan, 2012. "A direct approach to sparse discriminant analysis in ultra-high dimensions," Biometrika, Biometrika Trust, vol. 99(1), pages 29-42.
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