Related papers: On Low-Rank Hankel Matrix Denoising
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
Many statistical studies are concerned with the analysis of observations organized in a matrix form whose elements are count data. When these observations are assumed to follow a Poisson or a multinomial distribution, it is of interest to…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
Let $A$ be an $m \times n$ matrix with rank $r$ and spectral decomposition $A = \sum_{i=1}^r \sigma_i u_i v_i^\top,$ where $\sigma_i$ are its singular values, ordered decreasingly, and $u_i, v_i$ are the corresponding left and right…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
We consider the problems of computing the optimal rank-$1$ Hankel and Toeplitz-structured approximation of arbitrary matrices under $L_2$ and $L_1$-norm error. Such problems arise naturally in engineered systems, including the basic…
This paper revisits the problem of decomposing a positive semidefinite matrix as a sum of a matrix with a given rank plus a sparse matrix. An immediate application can be found in portfolio optimization, when the matrix to be decomposed is…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…
We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…
Image denoising is a typical ill-posed problem due to complex degradation. Leading methods based on normalizing flows have tried to solve this problem with an invertible transformation instead of a deterministic mapping. However, the…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…
We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…