Nyström approximation of Wishart matrices

Spectral methods requiring the computation of eigenvalues and eigenvectors of a positive definite matrix are an essential part of signal processing. However, for sufficiently high-dimensional data sets, the eigenvalue problem cannot be solved without approximate methods. We examine a technique for approximate spectral analysis and low-rank matrix reconstruction known as the Nyström method, which recasts the eigendecomposition of large matrices as a subset selection problem. In particular, we focus on the performance of the Nyström method when used to approximate random matrices from the Wishart ensemble. We provide statistical results for the approximation error, as well as an experimental analysis of various subset sampling techniques.