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    A Large Dimensional Study of Regularized Discriminant Analysis

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    Type
    Article
    Authors
    Elkhalil, Khalil cc
    Kammoun, Abla
    Couillet, Romain
    Al-Naffouri, Tareq Y. cc
    Alouini, Mohamed-Slim cc
    KAUST Department
    Communication Theory Lab
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2020
    Permanent link to this record
    http://hdl.handle.net/10754/662431
    
    Metadata
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    Abstract
    In this paper, we conduct a large dimensional study of regularized discriminant analysis classifiers with its two popular variants known as regularized LDA and regularized QDA. The analysis is based on the assumption that the data samples are drawn from a Gaussian mixture model with different means and covariances and relies on tools from random matrix theory (RMT). We consider the regime in which both the data dimension and training size within each class tends to infinity with fixed ratio. Under mild assumptions, we show that the probability of misclassification converges to a deterministic quantity that describes in closed form the performance of these classifiers in terms of the class statistics as well as the problem dimension. The result allows for a better understanding of the underlying classification algorithms in terms of their performances in practical large but finite dimensions. Further exploitation of the results permits to optimally tune the regularization parameter with the aim of minimizing the probability of misclassification. The analysis is validated with numerical results involving synthetic as well as real data from the USPS dataset yielding a high accuracy in predicting the performances and hence making an interesting connection between theory and practice.
    Citation
    Elkhalil, K., Kammoun, A., Couillet, R., Alnaffouri, T., & Alouini, M. (2020). A Large Dimensional Study of Regularized Discriminant Analysis. IEEE Transactions on Signal Processing, 1–1. doi:10.1109/tsp.2020.2984160
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Signal Processing
    DOI
    10.1109/TSP.2020.2984160
    Additional Links
    https://ieeexplore.ieee.org/document/9055087/
    https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9055087
    ae974a485f413a2113503eed53cd6c53
    10.1109/TSP.2020.2984160
    Scopus Count
    Collections
    Articles; Electrical and Computer Engineering Program; Communication Theory Lab; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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