Fluctuations of spiked random matrix models and failure diagnosis in sensor networks

TL;DR

This paper analyzes the fluctuations of extreme eigenvalues and eigenvectors in spiked random matrix models and applies these findings to detect and diagnose failures in large sensor networks.

Contribution

It provides a new theoretical framework linking eigenvalue fluctuations in spiked models to failure detection in sensor networks.

Findings

Eigenvalue fluctuations follow a CLT for unit multiplicity spikes.

Asymptotic fluctuations relate to GUE matrices.

Framework enables detection of known or unknown failure magnitudes.

Abstract

In this article, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity matrix, corresponding to the so-called spiked model in random matrix theory. The asymptotic fluctuations, as the matrix size grows large, are shown to be intimately linked with matrices from the Gaussian unitary ensemble (GUE). When the spiked population eigenvalues have unit multiplicity, the fluctuations follow a central limit theorem. This result is used to develop an original framework for the detection and diagnosis of local failures in large sensor networks, for known or unknown failure magnitude.