Related papers: Theoretical Performance Analysis of Eigenvalue-bas…
In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
Cooperative spectrum sensing based on the limiting eigenvalue ratio of the covariance matrix offers superior detection performance and overcomes the noise uncertainty problem. While an exact expression exists, it is complex and multiple…
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…
This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the…
In this paper we derive and analyze two algorithms -- referred to as decentralized power method (DPM) and decentralized Lanczos algorithm (DLA) -- for distributed computation of one (the largest) or multiple eigenvalues of a sample…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
This paper introduces the Eigenvalue-Based Randomness (EBR) test - a novel approach rooted in the Tracy-Widom law from random matrix theory - and applies it to the context of residual analysis in panel data models. Unlike traditional…
We propose a method to efficiently estimate the eigenvalues of any arbitrary (potentially weighted and/or directed) network of interacting dynamical agents from dynamical observations. These observations are discrete, temporal measurements…
We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
While the design of automated knowledge-based sensor scheduling is relevant to many multi-target detection and tracking problems, tracking algorithms are rarely built for this purpose and their outputs provide little flexibility for the…
The detection problem in statistical signal processing can be succinctly formulated: Given m (possibly) signal bearing, n-dimensional signal-plus-noise snapshot vectors (samples) and N statistically independent n-dimensional noise-only…
In this paper, we propose an eigenvalue analysis -- of system dynamics models -- based on the Mutual Information measure, which in turn will be estimated via the Kernel Density Estimation method. We postulate that the proposed approach…
In this paper, High-dimensional data analysis methods are proposed to deal with random matrix which is composed by the real data from power network before and after the fault. The mean spectral radius (MSR) of non-Hermitian random matrices…
The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form…
This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…