# Nonparametric Linear Discriminant Analysis for High Dimensional Matrix-Valued Data

arXiv: https://arxiv.org/abs/2507.19028 · HTML: https://mlsanity.com/paper/2507.19028/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [Covariate-Adjusted Tensor Classification in High-Dimensions](https://mlsanity.com/paper/1805.04421/) (2018)
- [Matrix Linear Discriminant Analysis](https://mlsanity.com/paper/1809.08746/) (2018)
- [Classification with the matrix-variate-t distribution](https://mlsanity.com/paper/1907.09565/) (2019)
- [Covariance Estimation for Matrix-valued Data](https://mlsanity.com/paper/2004.05281/) (2020)
- [Approximate nonparametric maximum likelihood inference for mixture models via convex optimization](https://mlsanity.com/paper/1606.02011/) (2016)
- [A penalized likelihood method for classification with matrix-valued predictors](https://mlsanity.com/paper/1609.07386/) (2016)

## Abstract (arXiv)

This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal distribution, we propose a novel extension of Fisher's Linear Discriminant Analysis (LDA) tailored for matrix-valued observations. To effectively capture structural information while maintaining estimation flexibility, we adopt a nonparametric empirical Bayes framework based on Nonparametric Maximum Likelihood Estimation (NPMLE), applied to vectorized and scaled matrices. The NPMLE method has been shown to provide robust, flexible, and accurate estimates for vector-valued data with various structures in the mean vector or covariance matrix. By leveraging its strengths, our method is effectively generalized to the matrix setting, thereby improving classification performance. Through extensive simulation studies and real data applications, including electroencephalography (EEG) and magnetic resonance imaging (MRI) analysis, we demonstrate that the proposed method tends to outperform existing approaches across a variety of data structures.