Sparse subspace linear discriminant analysis

We study high dimensional multigroup classification from a sparse subspace estimation perspective, unifying the linear discriminant analysis (LDA) with other recent developments in high dimensional multivariate analysis using similar tools, such as penalization method. We develop two two-stage sparse LDA models, where in the first stage, convex relaxation is used to convert two classical formulations of LDA to semidefinite programs, and furthermore subspace perspective allows for straightforward regularization and estimation. After the initial convex relaxation, we use a refinement stage to improve the accuracy. For the first model, a penalized quadratic program with group lasso penalty is used for refinement, whereas a sparse version of the power method is used for the second model. We carefully examine the theoretical properties of both methods, alongside with simulations and real data analysis.