Sr-LDA:Sparse and Reduced-Rank Linear Discriminant Analysis for High Dimensional Matrix

High-dimensional matrix-valued data is common in scientific and engineering studies and its classification is a significant topic in current statistics. In practice, the discriminative signals of the matrix covariates are oftentimes low rank and sparse. Motivated by this, we propose a sparse and reduced-rank matrix linear discriminant analysis called "Sr-LDA" for binary classification of high-dimensional matrix-valued data. Specifically, based on the Bayes' linear discriminant rule, we derive the theoretically optimal discriminative matrix-valued covariates under the matrix normal assumptions, and constructed a convex empirical loss function for the estimation of the optimal discriminative matrix-valued covariates under the $\ell _{1}$ -norm and nuclear norm penalties. Finite sample error bounds for parameter estimation and the misclassification rate are established. The superior performance of the proposed Sr-LDA is illustrated via extensive simulation and real data studies with comparison to other state-of-the-art classifiers.