# A penalized likelihood method for classification with matrix-valued predictors

arXiv: https://arxiv.org/abs/1609.07386 · HTML: https://mlsanity.com/paper/1609.07386/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2016.

## Built on by (most cited first, 1 of 1)

- [Nonparametric Linear Discriminant Analysis for High Dimensional Matrix-Valued Data](https://mlsanity.com/paper/2507.19028/) (2025)

## Abstract (arXiv)

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.