DC programming and DCA for sparse Fisher linear discriminant analysis

We consider the supervised pattern classification in the high-dimensional setting, in which the number of features is much larger than the number of observations. We present a novel approach to the sparse Fisher linear discriminant problem using the ℓ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _0$$\end{document}-norm. The resulting optimization problem is nonconvex, discontinuous and very hard to solve. We overcome the discontinuity by using appropriate approximations to the ℓ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _0$$\end{document}-norm such that the resulting problems can be formulated as difference of convex functions (DC) programs to which DC programming and DC Algorithms (DCA) are investigated. The experimental results on both simulated and real datasets demonstrate the efficiency of the proposed algorithms compared to some state-of-the-art methods.