Sparse Uncorrelated Linear Discriminant Analysis

In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum \ell_1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a \ell_1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in low-dimensional space.