Matrix Linear Discriminant Analysis

TL;DR

This paper introduces a new matrix linear discriminant analysis method for high-dimensional imaging data, leveraging nuclear norm penalization to promote low-rank solutions, with proven theoretical guarantees and superior empirical performance.

Contribution

It presents a novel nuclear norm penalized regression approach for matrix LDA, with theoretical analysis and demonstrated advantages over existing methods.

Findings

The method achieves low non-asymptotic risk bounds.

It demonstrates rank consistency in high-dimensional settings.

Empirical results show improved classification accuracy on EEG data.

Abstract

We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a non-asymptotic risk bound and a rank consistency result are established. Simulation studies and an application to electroencephalography data show the superior performance of the proposed method over the existing approaches.