相关论文: Spectral Ergodicity in Deep Learning Architectures…

Ensemble learning is a methodology that integrates multiple DNN learners for improving prediction performance of individual learners. Diversity is greater when the errors of the ensemble prediction is more uniformly distributed. Greater…

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…

Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…

Network geometries are typically characterized by having a finite spectral dimension (SD), $d_{s}$ that characterizes the return time distribution of a random walk on a graph. The main purpose of this work is to determine the SD of a…

An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…

In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…

Deep representation learning is a crucial procedure in multimedia analysis and attracts increasing attention. Most of the popular techniques rely on convolutional neural network and require a large amount of labeled data in the training…

We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of $n$ random points in a compact set $\Omega_n$ of $\R^d$. Under various assumptions we establish the…

Multifractal analysis is a powerful approach for characterizing ergodic or localized nature of eigenstates in complex quantum systems. In this context, the eigenvectors of random matrices belonging to invariant ensembles naturally serve as…

We consider stochastic smoothing of spectral functions of matrices using perturbations commonly studied in random matrix theory. We show that a spectral function remains spectral when smoothed using a unitarily invariant perturbation…

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

We study spectral algorithms in the setting where kernels are learned from data. We introduce the effective span dimension (ESD), an alignment-sensitive complexity measure that depends jointly on the signal, spectrum, and noise level…

Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…

We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…

In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the…

Consider $N\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \geq N^{3/4+\varepsilon}$ for any $\varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we…

Network embedding aims to learn low-dimensional representations of nodes in a network, while the network structure and inherent properties are preserved. It has attracted tremendous attention recently due to significant progress in…

Spectral clustering is one of the most popular algorithms for community detection in network analysis. Based on this rationale, in this paper we give the convergence rate of eigenvectors for the adjacency matrix in the $l_\infty$ norm,…

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…

Spectral methods include a family of algorithms related to the eigenvectors of certain data-generated matrices. In this work, we are interested in studying the geometric landscape of the eigendecomposition problem in various spectral…