Random Matrix Theory and the Informational Limit of Eigen-analysis

Professor Raj Rao Radakuditi

EECS Department

University of Michigan

Abstract:

Motivated by the ubiquity of signal-plus-noise type models in high-dimensional statistical

signal processing and machine learning, we consider the (noisy) eigenvalues and eigenvectors

of low-rank "signal" matrices that are corrupted by "noise" random matrices. Applications in

mind are as diverse as radar, sonar, wireless communications, matrix completion, spectral

clustering, bio-informatics and Gaussian mixture cluster analysis in machine learning.

We provide an application-independent approach that brings into sharp focus a fundamental

informational limit of the recovery of the low-dimensional signal subspaces (or matrices)

using eigen-analysis. Continuing on this success, we highlight the random matrix origin of this

informational limit, the connection with "free" harmonic analysis and discuss implications for

high-dimensional statistical signal processing and learning.

Biography:

R. R. Nadakuditi is an Assistant Professor of EECS at the University of Michigan. He received

his PhD in 2007 from MIT. His research lies at the interface of statistical signal processing and

random matrix theory with applications to sonar, radar, wireless communications and machine

learning.

For more information contact Prof. Ali Sayed (sayed@ee.ucla.edu)