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This work studies the theoretical rules of feature selection in lineardiscriminant analysis (LDA), and a new feature selection method is proposed forsparse linear discriminant analysis. An $l_1$ minimization method is used toselect the important features from which the LDA will be constructed. Theasymptotic results of this proposed two-stage LDA (TLDA) are studied,demonstrating that TLDA is an optimal classification rule whose convergencerate is the best compared to existing methods. The experiments on simulated andreal datasets are consistent with the theoretical results and show that TLDAperforms favorably in comparison with current methods. Overall, TLDA uses alower minimum number of features or genes than other approaches to achieve abetter result with a reduced misclassification rate.

Optimal feature selection for sparse linear discriminant analysis and its applications in gene expression data