A penalized likelihood method for classification with matrix-valued predictors

TL;DR

This paper introduces a penalized likelihood approach for classification with matrix-valued predictors, estimating means and a Kronecker-structured precision matrix, improving interpretability and accuracy in EEG data analysis.

Contribution

It presents a novel penalized likelihood method that leverages Kronecker structure for efficient estimation in matrix predictor classification tasks.

Findings

Outperforms relevant competitors in classification accuracy.

Demonstrates interpretability on EEG dataset.

Effective even when modeling assumptions are violated.

Abstract

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.