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Optimal feature selection for sparse linear discriminant analysis and its applications in gene expression data

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  • Wang, Cheng
  • Cao, Longbing
  • Miao, Baiqi

Abstract

This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An l1 minimization method is used to select the important features from which the LDA will be constructed. The asymptotic results of this proposed two-stage LDA (TLDA) are studied, demonstrating that TLDA is an optimal classification rule whose convergence rate is the best compared to existing methods. The experiments on simulated and real datasets are consistent with the theoretical results and show that TLDA performs favorably in comparison with current methods. Overall, TLDA uses a lower minimum number of features or genes than other approaches to achieve a better result with a reduced misclassification rate.

Suggested Citation

  • Wang, Cheng & Cao, Longbing & Miao, Baiqi, 2013. "Optimal feature selection for sparse linear discriminant analysis and its applications in gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 140-149.
    • Handle: RePEc:eee:csdana:v:66:y:2013:i:c:p:140-149
    DOI: 10.1016/j.csda.2013.04.003
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    References listed on IDEAS

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    1. 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.
    2. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    3. 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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    1. Li-Pang Chen, 2022. "Classification and prediction for multi-cancer data with ultrahigh-dimensional gene expressions," PLOS ONE, Public Library of Science, vol. 17(9), pages 1-25, September.
    2. Luigi Ippoliti & Simone Di Zio & Arcangelo Merla, 2014. "Classification of biomedical signals for differential diagnosis of Raynaud's phenomenon," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1830-1847, August.
    3. Jiang, Binyan & Leng, Chenlei, 2016. "High dimensional discrimination analysis via a semiparametric model," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 103-110.

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