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    Asymptotic performance of regularized quadratic discriminant analysis based classifiers

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    Type
    Conference Paper
    Authors
    Elkhalil, Khalil cc
    Kammoun, Abla cc
    Couillet, Romain
    Al-Naffouri, Tareq Y. cc
    Alouini, Mohamed-Slim cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2017-12-13
    Online Publication Date
    2017-12-13
    Print Publication Date
    2017-09
    Permanent link to this record
    http://hdl.handle.net/10754/626960
    
    Metadata
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    Abstract
    This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
    Citation
    Elkhalil K, Kammoun A, Couillet R, Al-Naffouri TY, Alouini M-S (2017) Asymptotic performance of regularized quadratic discriminant analysis based classifiers. 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP). Available: http://dx.doi.org/10.1109/MLSP.2017.8168172.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP)
    DOI
    10.1109/MLSP.2017.8168172
    Additional Links
    http://ieeexplore.ieee.org/document/8168172/
    ae974a485f413a2113503eed53cd6c53
    10.1109/MLSP.2017.8168172
    Scopus Count
    Collections
    Conference Papers; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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