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A Singular Value Thresholding Algorithm for Matrix Completion

by Jian-Feng Cai, Emmanuel J. Candès, Zuowei Shen , 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 ..."
Abstract - Cited by 555 (22 self) - Add to MetaCart
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

Exact Matrix Completion via Convex Optimization

by Emmanuel J. Candès, Benjamin Recht , 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 ..."
Abstract - Cited by 873 (26 self) - Add to MetaCart
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

by Emmanuel J. Candès, Yaniv Plan
"... 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 ..."
Abstract - Cited by 255 (13 self) - Add to MetaCart
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

The Power of Convex Relaxation: Near-Optimal Matrix Completion

by Emmanuel J. Candès, Terence Tao , 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 ..."
Abstract - Cited by 359 (7 self) - Add to MetaCart
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

by Jared Tanner, Joint Blanchard, Jared Tanner, Jared Tanner, Jared Tanner, Jared Tanner
"... 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

by Benjamin Recht - 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 ..."
Abstract - Cited by 158 (6 self) - Add to MetaCart
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

by Natali Ruchansky, Mark Crovella, Evimaria Terzi , 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 data-analysis 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 data-analysis task for these datasets is matrix completion, where the goal is to accurately infer the entries missing from

Incoherence-optimal matrix completion

by Yudong Chen , 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 order-wise optimal with respect to the ..."
Abstract - Cited by 16 (3 self) - Add to MetaCart
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 order-wise optimal with respect

Computational limits for matrix completion

by Moritz Hardt, Raghu Meka, Prasad Raghavendra, Benjamin Weitz - CoRR
"... 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. A ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
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

Universal Matrix Completion

by Srinadh Bhojanapalli
"... 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: ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
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
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