  We propose a penalized likelihood method to fit the linear discriminant
analysis model when the predictor is matrix valued. We simultaneously estimate
the means and the precision matrix, which we assume has a Kronecker product
decomposition. Our penalties encourage pairs of response category mean matrices
to have equal entries and also encourage zeros in the precision matrix. To
compute our estimators, we use a blockwise coordinate descent algorithm. To
update the optimization variables corresponding to response category mean
matrices, we use an alternating minimization algorithm that takes advantage of
the Kronecker structure of the precision matrix. We show that our method can
outperform relevant competitors in classification, even when our modeling
assumptions are violated. We analyze an EEG dataset to demonstrate our method's
interpretability and classification accuracy.
