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High dimensional discriminant analysis using sparse covariance estimator

  • Author / Creator
    Zhang, Jiaxin
  • High dimensional classification has drawn massive attention due to its increasing application in genetic
    diagnosis, image or speech recognition and financial analysis. Traditional methods such as Linear Discriminant
    Analysis (LDA) and Quadratic Discriminant Analysis (QDA), which are optimal Bayes classifiers
    under normality assumption, sometimes fail in high dimensional space where the number of variables
    is considerably greater than the sample size, and thus it is impossible to obtain a good estimation of the
    covariance matrix by using the conventional empirical estimator. An alternative approach is Naive Bayes
    which instead assumes all features are independent. Although independence is a critical assumption, it
    surprisingly does work well in many practical cases. Inspired by the success of Naive Bayes, we aim to
    find a balance between Naive Bayes and LDA. Hence, it is reasonable to assume only few correlations
    between features exist in high dimension so that we can take advantage of the sparsity and get a better covariance
    estimator. The main contribution of this thesis is that we improved the conventional LDA under
    the sparsity assumption by replacing the empirical covariance estimator with a sparse one. We also review
    various classification methods specific for high dimensional space. We compared our approach with some
    of these methods available in R with both simulation and two real data sets and the result showed that our
    method outperformed many baselines.

  • Subjects / Keywords
  • Graduation date
    Fall 2019
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-y2ft-c247
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.