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A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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remarkable features making this attractive for lowrank matrix completion problems. The first is that the softthresholding 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
Exact Matrix Completion via Convex Optimization
, 2008
"... 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 perfe ..."
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Cited by 873 (26 self)
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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
Matrix Completion with Noise
"... On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest ..."
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Cited by 255 (13 self)
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completion, which shows that under some suitable conditions, one can recover an unknown lowrank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclearnorm minimization subject to data constraints. Further, this paper introduces novel results showing
The Power of Convex Relaxation: NearOptimal Matrix Completion
, 2009
"... 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. In ..."
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Cited by 359 (7 self)
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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
Matrix completion
"... 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 fast ..."
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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?
A simpler approach to matrix completion
 the Journal of Machine Learning Research
"... 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 by minim ..."
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Cited by 158 (6 self)
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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
Matrix Completion with Queries
, 2015
"... 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 dataanalysis task for these datasets is matrix completion, where the goal is to accurately infer the entries missing from the ma ..."
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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 dataanalysis task for these datasets is matrix completion, where the goal is to accurately infer the entries missing from
Incoherenceoptimal matrix completion
, 2013
"... This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is orderwise optimal with respect to the ..."
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Cited by 16 (3 self)
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This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is orderwise optimal with respect
Computational limits for matrix completion
 CoRR
"... Matrix Completion is the problem of recovering an unknown realvalued lowrank 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. A ..."
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Cited by 2 (1 self)
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Matrix Completion is the problem of recovering an unknown realvalued lowrank 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
Universal Matrix Completion
"... The problem of lowrank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite restrictive in practice. More specifically, the methods assume that: ..."
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Cited by 3 (0 self)
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The problem of lowrank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite restrictive in practice. More specifically, the methods assume that
Results 1  10
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