Related papers: Uniqueness of Low Rank Matrix Completion and Schur…

Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and…

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion…

We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An…

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…

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…

The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…

We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if…