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A Note on the Connection and Equivalence of Three Sparse Linear Discriminant Analysis Methods

Summary: In this article, we reveal the connection between and equivalence of three sparse linear discriminant analysis methods: the 1-Fisher’s discriminant analysis proposed by Wu et al. in 2008, the sparse optimal scoring proposed by Clemmensen et al. in 2011, and the direct sparse discriminant analysis (DSDA) proposed by Mai et al. in 2012. It is shown that, for any sequence of penalization parameters, the normalized solutions of DSDA equal the normalized solutions of the other two methods at different penalization parameters. A prostate cancer dataset is used to demonstrate the theory.

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  • Topics: Quality Tools, Statistics
  • Keywords: Discriminant analysis, Biomedical, Medical, Classification, Sparse optimal scoring,
  • Author: Mai, Qing; Zou, Hui;
  • Journal: Technometrics