Electrical Engineering Systems Seminar

Motivated by signal-plus-noise type models in high-dimensional statistical signal processing and machine learning, we consider the eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices.

Applications in mind are as diverse as radar, sonar, wireless communications, 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 high-dimensional 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.