  We propose a novel linear discriminant analysis approach for the
classification of high-dimensional matrix-valued data that commonly arises from
imaging studies. Motivated by the equivalence of the conventional linear
discriminant analysis and the ordinary least squares, we consider an efficient
nuclear norm penalized regression that encourages a low-rank structure.
Theoretical properties including a non-asymptotic risk bound and a rank
consistency result are established. Simulation studies and an application to
electroencephalography data show the superior performance of the proposed
method over the existing approaches.
