Related papers: A computational study of low precision incomplete …
The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…
This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
This paper concerns a class of DC composite optimization problems which, as an extension of convex composite optimization problems and DC programs with nonsmooth components, often arises in robust factorization models of low-rank matrix…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies in solving large-scale sparse symmetric positive definite…
In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…
This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information.…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled…
Completing multidimensional tensor-structured data with missing entries is a fundamental task for many real-world applications involving incomplete or corrupted datasets. For data with spatial or temporal side information, low-rank…