Related papers: Algebraic Variety Models for High-Rank Matrix Comp…

The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…

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…

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…

We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…

We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank of the unknown target matrix is known in advance. In this paper, first we revisit a recently proposed rank-based…

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…

In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…

We consider the problem of reconstructing a rank-$k$ $n \times n$ matrix $M$ from a sampling of its entries. Under a certain incoherence assumption on $M$ and for the case when both the rank and the condition number of $M$ are bounded, it…

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

It was recently shown that low rank matrix completion theory can be employed for designing new sampling schemes in the context of MIMO radars, which can lead to the reduction of the high volume of data typically required for accurate target…

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…

This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development…

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…

In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…