Related papers: Spectral Estimation with Free Decompression

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…

In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…

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…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…

A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random…

Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of…

Exact eigendecomposition of large matrices is very expensive, and it is practically impossible to compute exact eigenvalues. Instead, one may set a more modest goal of approaching the empirical distribution of the eigenvalues, recovering…

This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector…

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…

We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process…

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…

Spectral methods which represent data points by eigenvectors of kernel matrices or graph Laplacian matrices have been a primary tool in unsupervised data analysis. In many application scenarios, parametrizing the spectral embedding by a…

The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to…

We propose a novel estimation procedure for certain spectral distributions associated with a class of high dimensional linear time series. The processes under consideration are of the form $X_t = \sum_{\ell=0}^\infty \mathbf{A}_\ell…

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…

We address the subset selection problem for matrices, where the goal is to select a subset of $k$ columns from a "short-and-fat" matrix $X \in \mathbb{R}^{m \times n}$, such that the pseudoinverse of the sampled submatrix has as small…

Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…

This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…