Matrix Linear Discriminant Analysis
This addresses classification challenges in fields like medical imaging, though it is incremental as it builds on existing linear discriminant analysis methods.
The authors tackled the classification of high-dimensional matrix-valued data, such as from imaging studies, by proposing a novel linear discriminant analysis method using nuclear norm penalized regression, which achieved superior performance in simulations and an EEG application.
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.