Matrix Linear Discriminant Analysis

Abstract

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.

Keywords:

• Linear discriminant analysis
• Low rank
• Matrix data
• Nuclear norm
• Rank consistency
• Risk bound

Acknowledgments

The authors would like to thank the Editor, Associate Editor and two reviewers for their constructive comments, which have substantially improved the article.

Additional information

Funding

Shen’s research is partially supported by Simons Foundation Award 512620 and NSF DMS-1509023. Zhou’s research is partially supported by NIH grants R01HG006139, R01GM53275 and NSF DMS-1310319. Kong’s research is partially supported by the Natural Science and Engineering Research Council of Canada.