Singular Value Decomposition and High Dimensional Data

Abstract

Abstract The singular value decomposition and related principal components analysis are foundational multivariate methods used for dimension reduction and exploratory analysis of high‐dimensional data. Studying this decomposition using random matrix theory, however, reveals troubling behavior when the number of variables is larger than the number of samples. This article surveys random matrix theory results related to the singular value decomposition and high‐dimensional data as well as recent developments such as sparse principal components analysis. Software on the random matrix theory distributions related to the singular value decomposition can be found elsewhere; several software packages implementing methods for sparse principal components analysis are also available.