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    Asymptotic Performance of Linear Discriminant Analysis with Random Projections

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    Type
    Conference Paper
    Authors
    Elkhalil, Khalil cc
    Kammoun, Abla cc
    Calderbank, Robert
    Al-Naffouri, Tareq Y. cc
    Alouini, Mohamed-Slim cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering
    Electrical Engineering Program
    Date
    2019-05
    Permanent link to this record
    http://hdl.handle.net/10754/655964
    
    Metadata
    Show full item record
    Abstract
    We investigate random projections in the context of randomly projected linear discriminant analysis (LDA). We consider the case in which the data of dimension p is randomly projected onto a lower dimensional space before being fed to the classifier. Using fundamental results from random matrix theory and relying on some mild assumptions, we show that the asymptotic performance in terms of probability of misclassification approaches a deterministic quantity that only depends on the data statistics and the dimensions involved. Such results permits to reliably predict the performance of projected LDA as a function of the reduced dimension d < p and thus helps to determine the minimum d to achieve a certain desired performance. Finally, we validate our results with finite-sample settings drawn from both synthetic data and the popular MNIST dataset.
    Citation
    Elkhalil, K., Kammoun, A., Calderbank, R., Al-Naffouri, T. Y., & Alouini, M.-S. (2019). Asymptotic Performance of Linear Discriminant Analysis with Random Projections. ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). doi:10.1109/icassp.2019.8683386
    Sponsors
    The authors thank Vahid Tarokh for valuable discussions.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Conference/Event name
    ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
    DOI
    10.1109/ICASSP.2019.8683386
    Additional Links
    https://ieeexplore.ieee.org/document/8683386/
    https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8683386
    ae974a485f413a2113503eed53cd6c53
    10.1109/ICASSP.2019.8683386
    Scopus Count
    Collections
    Conference Papers; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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