remarkable features making this attractive for low-rank matrix completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal

We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can

completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing

This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering

Universality using cluster: embarrassingly Empirical testing of iterative algorithms using GPUs Three sparse approximation questions to test Sparse approximation: min x ‖x‖0 s.t. ‖Ax − b‖2 ≤ τ with A ∈ R m×n 1. Are there algorithms that have same behaviour for different A? 2. Which algorithm is fastest and with a high recovery probability?

This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candès and Recht [4], Candès and Tao [7], and Keshavan, Montanari, and Oh [18]. The reconstruction is accomplished

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 goal is to accurately infer the entries missing from

In this paper, we consider the matrix completion problem when the observations are one-bit mea-surements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender sys-tems and social

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is incoherent and the subsample is drawn uniformly at random

The problem of low-rank matrix completion has recently generated a lot of interest leading to sev-eral results that offer exact solutions to the prob-lem. However, in order to do so, these methods make assumptions that can be quite restrictive in practice. More specifically, the methods assume that