Matrix Linear Discriminant Analysis

We propose a novel linear discriminant analysis (LDA) approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional LDA and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a nonasymptotic 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.

本文提出一种新颖的线性判别分析（linear discriminant analysis, LDA）方法，用于分类成像研究中常见的高维矩阵值数据。受传统LDA与普通最小二乘法等价性的启发，本文构建了一种高效的核范数惩罚回归方法，该方法可诱导出低秩结构。本文确立了该方法的多项理论性质，涵盖非渐近风险界与秩一致性结果。仿真实验与脑电图（electroencephalography）数据的应用结果表明，相较于现有方法，本文所提方法具有更优异的性能。