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LowRank Matrix Completion
, 2013
"... While datasets are frequently represented as matrices, realword data is imperfect and entries are often missing. In many cases, the data are very sparse and the matrix must be filled in before any subsequent work can be done. This optimization problem, known as matrix completion, can be made welld ..."
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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 lowrank matrix completion. The first paper we review presents an iterative algorithm to
LowRank Matrix Approximation with Stability
"... Abstract Lowrank matrix approximation has been widely adopted in machine learning applications with sparse data, such as recommender systems. However, the sparsity of the data, incomplete and noisy, introduces challenges to the algorithm stability small changes in the training data may significan ..."
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Abstract Lowrank matrix approximation has been widely adopted in machine learning applications with sparse data, such as recommender systems. However, the sparsity of the data, incomplete and noisy, introduces challenges to the algorithm stability small changes in the training data may
DECENTRALIZED LOWRANK MATRIX COMPLETION
"... This paper introduces algorithms for the decentralized lowrank matrix completion problem. Assume a lowrank 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 mat ..."
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Cited by 5 (3 self)
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This paper introduces algorithms for the decentralized lowrank matrix completion problem. Assume a lowrank 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
Sparse and LowRank Matrix Decompositions
, 2009
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, but obtaining an ex ..."
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Cited by 31 (2 self)
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Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, but obtaining
Concentrationbased guarantees for lowrank matrix reconstruction
 24th Annual Conference on Learning Theory (COLT
, 2011
"... We consider the problem of approximately reconstructing a partiallyobserved, approximately lowrank matrix. This problem has received much attention lately, mostly using the tracenorm as a surrogate to the rank. Here we study lowrank matrix reconstruction using both the tracenorm, as well as the ..."
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Cited by 19 (5 self)
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We consider the problem of approximately reconstructing a partiallyobserved, approximately lowrank matrix. This problem has received much attention lately, mostly using the tracenorm as a surrogate to the rank. Here we study lowrank matrix reconstruction using both the tracenorm, as well
Information theoretic bounds for lowrank matrix completion
 in 2010 IEEE International Symposium on Information Theory (ISIT 2010
, 2010
"... Abstract—This paper studies the lowrank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) lowrank matrix source over an erasure channel. The paper then uses achievability and converse arguments to pr ..."
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Cited by 7 (1 self)
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Abstract—This paper studies the lowrank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) lowrank matrix source over an erasure channel. The paper then uses achievability and converse arguments
Exact Lowrank Matrix Recovery via Nonconvex
"... The lowrank matrix recovery (LMR) arises in many fields such as signal and image processing, statistics, computer vision, system identification and control, and it is NPhard. It is known that under some restricted isometry property (RIP) conditions we can obtain the exact lowrank matrix solution ..."
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Cited by 2 (0 self)
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The lowrank matrix recovery (LMR) arises in many fields such as signal and image processing, statistics, computer vision, system identification and control, and it is NPhard. It is known that under some restricted isometry property (RIP) conditions we can obtain the exact lowrank matrix solution
Robust LowRank Matrix Completion by Riemannian Optimization
"... Lowrank matrix completion is the problem where one tries to recover a lowrank 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 lowrank matrix completion, i.e., matrix completion where a fraction of the observ ..."
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Cited by 1 (1 self)
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Lowrank matrix completion is the problem where one tries to recover a lowrank 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 lowrank matrix completion, i.e., matrix completion where a fraction
Local LowRank Matrix Approximation
"... 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 lowrank. We propose a new matrix approximation model where we assume instead that the matrix is ..."
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Cited by 5 (1 self)
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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 lowrank. We propose a new matrix approximation model where we assume instead that the matrix
LowRank Matrix Recovery With Poisson Noise
"... Estimating an image M ∗ ∈ Rm1×m2+ from its linear measurements under Poisson noise is an important problem arises from applications such as optical imaging, nuclear medicine and xray imaging [1]. When the image M ∗ has a lowrank structure, we can use a small number of linear measurements to reco ..."
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to recover M∗, also known as lowrank 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 lowrank matrix recovery and completion under Gaussian noise
Results 1  10
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