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An adapted linear discriminant analysis with variable selection for the classification in high-dimension, and an application to medical data

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  • Le, Khuyen T.
  • Chaux, Caroline
  • Richard, Frédéric J.P.
  • Guedj, Eric

Abstract

The classification of normally distributed data in a high-dimensional setting when variables are more numerous than observations is considered. Under the assumption that the inverse covariance matrices (the precision matrices) are the same over all groups, the method of the linear discriminant analysis (LDA) is adapted by including a sparse estimate of these matrices. Furthermore, a variable selection procedure is developed based on the graph associated to the estimated precision matrix. For that, a discriminant capacity is defined for each connected component of the graph, and variables of the most discriminant components are kept. The adapted LDA and the variable selection procedure are both evaluated on synthetic data, and applied to real data from PET brain images for the classification of patients with Alzheimer’s disease.

Suggested Citation

  • Le, Khuyen T. & Chaux, Caroline & Richard, Frédéric J.P. & Guedj, Eric, 2020. "An adapted linear discriminant analysis with variable selection for the classification in high-dimension, and an application to medical data," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:csdana:v:152:y:2020:i:c:s0167947320301225
    DOI: 10.1016/j.csda.2020.107031
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    References listed on IDEAS

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    Cited by:

    1. Michael Fop & Pierre-Alexandre Mattei & Charles Bouveyron & Thomas Brendan Murphy, 2022. "Unobserved classes and extra variables in high-dimensional discriminant analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 55-92, March.
    2. Rasoul Lotfi & Davood Shahsavani & Mohammad Arashi, 2022. "Classification in High Dimension Using the Ledoit–Wolf Shrinkage Method," Mathematics, MDPI, vol. 10(21), pages 1-13, November.

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