A Direct Estimation Approach to Sparse Linear Discriminant Analysis

This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix and the difference of the mean vectors, we introduce a simple and effective classifier by estimating the product directly through constrained 1 minimization. The estimator can be implemented efficiently using linear programming and the resulting classifier is called the linear programming discriminant (LPD) rule.