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Sparse quadratic classification rules via linear dimension reduction

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  • Gaynanova, Irina
  • Wang, Tianying

Abstract

We consider the problem of high-dimensional classification between two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on the original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework does not require the estimation of precision matrices; it scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparisons with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of the ESR1 gene in differentiating estrogen receptor status.

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  • Gaynanova, Irina & Wang, Tianying, 2019. "Sparse quadratic classification rules via linear dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 278-299.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:278-299
    DOI: 10.1016/j.jmva.2018.09.011
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    References listed on IDEAS

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    1. Irina Gaynanova & James G. Booth & Martin T. Wells, 2016. "Simultaneous Sparse Estimation of Canonical Vectors in the ≫ Setting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 696-706, April.
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    5. Patrick Danaher & Pei Wang & Daniela M. Witten, 2014. "The joint graphical lasso for inverse covariance estimation across multiple classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 373-397, March.
    6. 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.
    7. Rukhin, Andrew L., 1992. "Generalized Bayes estimators of a normal discriminant function," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 154-162, April.
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    Cited by:

    1. Michael O. Olusola & Sydney I. Onyeagu, 2020. "On the binary classification problem in discriminant analysis using linear programming methods," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 119-130.
    2. Wu, Ruiyang & Hao, Ning, 2022. "Quadratic discriminant analysis by projection," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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