A penalized likelihood method for classification with matrix-valued predictors
This work addresses classification challenges in domains like neuroscience where predictors are matrices, but it is incremental as it builds on existing penalized likelihood and Kronecker product methods.
The authors tackled the problem of classification with matrix-valued predictors by proposing a penalized likelihood method for linear discriminant analysis, which simultaneously estimates means and a Kronecker-structured precision matrix, and they showed it outperforms competitors in classification accuracy, even when assumptions are violated, as demonstrated on an EEG dataset.
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.