Abstract: A common theme among high-dimensional linear discriminant analysis (LDA) methods is the sparsity assumption. However, in practice, this assumption may be violated, making sparse methods inaccurate. Motivated by this challenge, we propose a novel high-dimensional LDA method that relaxes the sparsity assumption. We assume that there exist a few sparse signals with large effects, and a large number of dense signals with small effects. In the parameter estimation, we combine the group Lasso penalty and the 𝓁₂ penalty to identify these signals automatically. Our estimation involves a convex optimization problem that can be solved straightforwardly. Theoretical and numerical results support the application of our proposal.

Key words and phrases: Group Lasso, 𝓁₂ penalty, linear discriminant analysis, regularization.