2018/02/10 by Zenan Ling, Robert C. Qiu, Ling, Zenan +5
Computer Science · Engineering · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Random Matrices and Applications #Signal Processing (eess.SP) #eess.SP #electronic engineering #information engineering #stat.AP
paper · pdf · doi:10.48550/arxiv.1802.03503
12 pages, 13 figures, submitted to IEEE Trans on Big Data
arxiv created 2018/02/10 · openalex publication_date 2018/02/10 · arxiv updated 2018/02/13 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28
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.