Related papers: A Rank-Corrected Procedure for Matrix Completion w…

This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size.…

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…

Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…

We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…

Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…

The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of color…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…

We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a…

The paper deals with the problem of penalized empirical risk minimization over a convex set of linear functionals on the space of Hermitian matrices with convex loss and nuclear norm penalty. Such penalization is often used in low rank…

Low rank matrix recovery is the focus of many applications, but it is a NP-hard problem. A popular way to deal with this problem is to solve its convex relaxation, the nuclear norm regularized minimization problem (NRM), which includes…

The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive…

We study the closure of the projection of the (nonconvex) cone of rank restricted positive semidefinite matrices onto subsets of the matrix entries. This defines the feasible sets for semidefinite completion problems with restrictions on…

Low-rank matrix completion is a problem of immense practical importance. Recent works on the subject often use nuclear norm as a convex surrogate of the rank function. Despite its solid theoretical foundation, the convex version of the…

This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…