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The maximal data piling direction for discrimination

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  • Jeongyoun Ahn
  • J. S. Marron

Abstract

We study a discriminant direction vector that generally exists only in high-dimension, low sample size settings. Projections of data onto this direction vector take on only two distinct values, one for each class. There exist infinitely many such directions in the subspace generated by the data; but the maximal data piling vector has the longest distance between the projections. This paper investigates mathematical properties and classification performance of this discrimination method. Copyright 2010, Oxford University Press.

Suggested Citation

  • Jeongyoun Ahn & J. S. Marron, 2010. "The maximal data piling direction for discrimination," Biometrika, Biometrika Trust, vol. 97(1), pages 254-259.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:1:p:254-259
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    File URL: http://hdl.handle.net/10.1093/biomet/asp084
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    Citations

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    Cited by:

    1. Chung, Hee Cheol & Ahn, Jeongyoun, 2021. "Subspace rotations for high-dimensional outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Ahn, Jeongyoun & Jeon, Yongho, 2015. "Sparse HDLSS discrimination with constrained data piling," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 74-83.
    3. Zhao, Junguang & Xu, Xingzhong, 2016. "A generalized likelihood ratio test for normal mean when p is greater than n," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 91-104.
    4. Gen Li & Sungkyu Jung, 2017. "Incorporating covariates into integrated factor analysis of multi‐view data," Biometrics, The International Biometric Society, vol. 73(4), pages 1433-1442, December.
    5. Jung, Sungkyu, 2018. "Continuum directions for supervised dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 27-43.
    6. 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.
    7. Makoto Aoshima & Kazuyoshi Yata, 2019. "Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 473-503, June.
    8. Yugo Nakayama & Kazuyoshi Yata & Makoto Aoshima, 2020. "Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1257-1286, October.
    9. Ursula Laa & Dianne Cook & Stuart Lee, 2020. "Burning Sage: Reversing the Curse of Dimensionality in the Visualization of High-Dimensional Data," Monash Econometrics and Business Statistics Working Papers 36/20, Monash University, Department of Econometrics and Business Statistics.
    10. Safo, Sandra E. & Ahn, Jeongyoun, 2016. "General sparse multi-class linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 81-90.
    11. Lee, Myung Hee, 2012. "On the border of extreme and mild spiked models in the HDLSS framework," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 162-168.

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