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Sparsifying the Fisher linear discriminant by rotation

Author

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  • Ning Hao
  • Bin Dong
  • Jianqing Fan

Abstract

type="main" xml:id="rssb12092-abs-0001"> Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis. To use them efficiently, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications, and rotations of data are required to create the sparsity needed. We propose a family of rotations to create the sparsity required. The basic idea is to use the principal components of the sample covariance matrix of the pooled samples and its variants to rotate the data first and then to apply an existing high dimensional classifier. This rotate-and-solve procedure can be combined with any existing classifiers and is robust against the level of sparsity of the true model. We show that these rotations do create the sparsity that is needed for high dimensional classifications and we provide theoretical understanding why such a rotation works empirically. The effectiveness of the method proposed is demonstrated by several simulated and real data examples, and the improvements of our method over some popular high dimensional classification rules are clearly shown.

Suggested Citation

  • Ning Hao & Bin Dong & Jianqing Fan, 2015. "Sparsifying the Fisher linear discriminant by rotation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 827-851, September.
  • Handle: RePEc:bla:jorssb:v:77:y:2015:i:4:p:827-851
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    File URL: http://hdl.handle.net/10.1111/rssb.2015.77.issue-4
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    Cited by:

    1. Sheng, Ying & Wang, Qihua, 2019. "Simultaneous variable selection and class fusion with penalized distance criterion based classifiers," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 138-152.
    2. Fujikoshi, Yasunori, 2022. "High-dimensional consistencies of KOO methods in multivariate regression model and discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. He, Yong & Zhang, Xinsheng & Wang, Pingping, 2016. "Discriminant analysis on high dimensional Gaussian copula model," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 100-112.
    4. Nickolay T. Trendafilov & Tsegay Gebrehiwot Gebru, 2016. "Recipes for sparse LDA of horizontal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 207-221, August.
    5. Rauf Ahmad, M. & Pavlenko, Tatjana, 2018. "A U-classifier for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 269-283.

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