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

  • discriminant analysis
  • sparsity
  • genomics data

• Graduation date

  Fall 2019

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-y2ft-c247

• License

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