Title: A New Approach of Exploiting Self-Adjoint Matrix Polynomials of Large Random Matrices for Anomaly Detection and Fault Location,
Abstract: Synchronized measurements of a large power grid enable an unprecedented
opportunity to study the spatialtemporal correlations. Statistical analytics
for those massive datasets start with high-dimensional data matrices.
Uncertainty is ubiquitous in a future's power grid. These data matrices are
recognized as random matrices. This new point of view is fundamental in our
theoretical analysis since true covariance matrices cannot be estimated
accurately in a high-dimensional regime. As an alternative, we consider
large-dimensional sample covariance matrices in the asymptotic regime to
replace the true covariance matrices. The self-adjoint polynomials of
large-dimensional random matrices are studied as statistics for big data
analytics. The calculation of the asymptotic spectrum distribution (ASD) for
such a matrix polynomial is understandably challenging. This task is made
possible by a recent breakthrough in free probability, an active research
branch in random matrix theory. This is the very reason why the work of this
paper is inspired initially. The new approach is interesting in many aspects.
The mathematical reason may be most critical. The real-world problems can be
solved using this approach, however.