相关论文: Spectral Properties of Infinitely Smooth Kernel Ma…

Kernel matrices are of central importance to many applied fields. In this manuscript, we focus on spectral properties of kernel matrices in the so-called ``flat limit'', which occurs when points are close together relative to the scale of…

Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…

Symmetric kernel matrices are a well-researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly…

In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the…

In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…

In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis. We present a set of concentration inequalities…

In this paper we analyse the spectrum of nonlocal Dirichlet problems with non-singular kernels in bounded open sets. The novelty is the continuity of eigenvalues with respect to domain perturbation via Lebesgue measure. Also, under…

The spectral gap of the graph Laplacian with Dirichlet boundary conditions is computed for the graphs of several communication networks at the IP-layer, which are subgraphs of the much larger global IP-layer network. We show that the…

Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…

Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…

Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…

In this paper, we take a fresh look at using spectral analysis for assessing locking phenomena in finite element formulations. We propose to "measure" locking by comparing the difference between eigenvalue and mode error curves computed on…

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…

In this paper, we focus on strongly local regular Dirichlet forms, especially those satisfying Morrey-type inequalities. We prove the equivalence between resistance estimates and heat kernel estimates in this case. Self-similar forms on…

We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…

Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently…

A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

We study the problem of super-resolution of a linear combination of Dirac distributions and their derivatives on a one-dimensional circle from noisy Fourier measurements. Following numerous recent works on the subject, we consider the…

Computing the eigenvectors and eigenvalues of a perturbed matrix can be remarkably difficult when the unperturbed matrix has repeated eigenvalues. In this work we show how the limiting eigenvectors and eigenvalues of a symmetric matrix…