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    Improved Design of Quadratic Discriminant Analysis Classi er in Unbalanced Settings

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    Type
    Dissertation
    Authors
    Bejaoui, Amine cc
    Advisors
    Alouini, Mohamed-Slim cc
    Committee members
    Huser, Raphaël G.
    Kammoun, Abla
    Program
    Statistics
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-04-23
    Permanent link to this record
    http://hdl.handle.net/10754/662639
    
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    Abstract
    The use of quadratic discriminant analysis (QDA) or its regularized version (RQDA) for classi cation is often not recommended, due to its well-acknowledged high sensitivity to the estimation noise of the covariance matrix. This becomes all the more the case in unbalanced data settings for which it has been found that R-QDA becomes equivalent to the classi er that assigns all observations to the same class. In this paper, we propose an improved R-QDA that is based on the use of two regularization parameters and a modi ed bias, properly chosen to avoid inappropriate behaviors of R-QDA in unbalanced settings and to ensure the best possible classi cation performance. The design of the proposed classi er builds on a re ned asymptotic analysis of its performance when the number of samples and that of features grow large simultaneously, which allows to cope e ciently with the high-dimensionality frequently met within the big data paradigm. The performance of the proposed classi er is assessed on both real and synthetic data sets and was shown to be much higher than what one would expect from a traditional R-QDA.
    Citation
    Bejaoui, A. (2020). Improved Design of Quadratic Discriminant Analysis Classi er in Unbalanced Settings. KAUST Research Repository. https://doi.org/10.25781/KAUST-97SG9
    DOI
    10.25781/KAUST-97SG9
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-97SG9
    Scopus Count
    Collections
    Dissertations; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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