Related papers: Localization and top eigenvalue detection
The detection and localization of a target from samples of its generated field is a problem of interest in a broad range of applications. Often, the target field admits structural properties that enable the design of lower sample detection…
This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…
We introduce a fresh scheme based on the local hidden variable models to quantify nonlocality for arbitrarily high-dimensional quantum systems. Our scheme explores the minimal amount of white noise that must be added to the system in order…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
Herein, the problem of simultaneous localization of two sources given a modest number of samples is examined. In particular, the strategy does not require knowledge of the target signatures of the sources a priori, nor does it exploit…
When physical systems are tunable by three classical parameters, level degeneracies may occur at isolated points in parameter space. A topological singularity in the phase of the degenerate eigenvectors exists at these points. When a path…
We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are…
Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in…
Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
A major focus of current research on place recognition is visual localization for autonomous driving. In this scenario, as cameras will be operating continuously, it is realistic to expect videos as an input to visual localization…
The eigenvalue shift technique is the most well-known and fundamental tool for matrix computations. Applications include the search of eigeninformation, the acceleration of numerical algorithms, the study of Google's PageRank. The shift…
We consider the problem of finding nonzero eigenvalues and the corresponding eigenvectors of a matrix $AA^{\top}$, where $A$ is a special incidence matrix; This matrix can equivalently be defined based on a match relation between some…
We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate…
Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…
We consider $N\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization…
For a Hamiltonian ${\hat H}$ containing a position-dependent (disordered) potential, we introduce a sequence of landscape functions $u_n(\vec{r})$ obeying ${\hat H} u_n(\vec{r}) = u_{n-1}(\vec{r})$ with $u_0(\vec{r}) = 1$. For $n \to…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…