On singular value distribution of large dimensional data matrices whose columns have different correlations

TL;DR

This paper studies the eigenvalue distribution of large data matrices with columns having different correlations, extending existing results under milder conditions and exploring applications in sample classification.

Contribution

It provides new insights into the spectral distribution of large correlated data matrices with relaxed moment conditions and discusses practical applications.

Findings

Derived spectral distribution under milder moment assumptions

Extended theoretical understanding of eigenvalues in correlated data matrices

Potential application in sample classification

Abstract

Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$ when $p$ increase with $n$ has been considered by some authors recently. This model has known an increasing popularity due to its widely applications in multi-user multiple-input single-output (MISO) systems and robust signal processing. In this paper, for more convenient applications in practice, we will investigate the spectral distribution of $\mathbf S_n$ under milder moment conditions than existing work. We also discuss a potential application in sample classification.