In this article, we reveal the connection between and equivalence of three sparse linear discriminant analysis methods: the ℓ1-Fishers 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.
Bibliographical noteFunding Information:
The authors thank the Editor, the Associate Editor, and two referees for their helpful comments and suggestions. This work is supported in part by NSF grant DMS-08-46068. The second author was supported by Fondecyt 11121131 grant.
- Direct sparse discriminant analysis
- Sparse optimal scoring
- ℓ 1-Fishers discriminant analysis