is convex and can be optimized efficiently, there has been a significant amount of research over the past few years to develop optimization algorithms that perform well. In this report, we review several methods for low-rank matrix completion. The first paper we review presents an iterative algorithm to

This paper introduces algorithms for the decentralized lowrank matrix completion problem. Assume a low-rank matrix W = [W1, W2,..., WL]. In a network, each agent ℓ observes some entries of Wℓ. In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, but obtaining

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well

Abstract—This paper studies the low-rank matrix completion problem from an information theoretic perspective. The comple-tion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper then uses achievability and converse arguments

The low-rank matrix recovery (LMR) arises in many fields such as signal and image processing, statistics, computer vision, system identification and control, and it is NP-hard. It is known that under some restricted isometry property (RIP) conditions we can obtain the exact low-rank matrix solution

Low-rank matrix completion is the problem where one tries to recover a low-rank matrix from noisy observations of a subset of its entries. In this paper, we propose RMC, a new method to deal with the problem of robust low-rank matrix completion, i.e., matrix completion where a fraction

Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix

This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are arbitrarily corrupted. We provide a new unified performance

to recover M∗, also known as low-rank matrix recovery. This is related to compressed sensing, where the goal is to develop efficient data acquisition systems by exploiting sparsity of underlying signals. While there has been much success for low-rank matrix recovery and completion under Gaussian noise