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1,399
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding
High dimensional graphs and variable selection with the Lasso
 ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
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Cited by 736 (22 self)
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show that the proposed neighborhood selection scheme is consistent for sparse highdimensional graphs. Consistency hinges on the choice of the penalty parameter. The oracle value for optimal prediction does not lead to a consistent neighborhood estimate. Controlling instead the probability of falsely
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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. In general, accurate recovery of a matrix from a small number of entries is impossible; but the knowledge that the unknown matrix has low rank radically changes this premise, making the search for solutions meaningful. This paper presents optimality results quantifying the minimum number of entries needed
Online learning for matrix factorization and sparse coding
, 2010
"... Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order to ad ..."
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Cited by 330 (31 self)
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Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order
Tag Completion for Image Retrieval
"... Abstract—Many social image search engines are based on keyword/tag matching. This is because tag based image retrieval (TBIR) is not only efficient but also effective. The performance of TBIR is highly dependent on the availability and quality of manual tags. Recent studies have shown that manual ta ..."
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Cited by 18 (1 self)
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of TBIR. To address this challenge, we study the problem of tag completion where the goal is to automatically fill in the missing tags as well as correct noisy tags for given images. We represent the imagetag relation by a tag matrix, and search for the optimal tag matrix consistent with both
An optimal online algorithm for metrical task systems
 JOURNAL OF THE ACM
, 1992
"... In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decision algorithm is developed. It is shown that, for an importan ..."
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Cited by 209 (8 self)
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, for an important algorithms. class of special cases, this algorithm is optimal among all online Specifically, a task system (S. d) for processing sequences of tasks consists of a set S of states and a cost matrix d where d(i, j) is the cost of changing from state i to state j (we assume that d satisfies
Infomax and Maximum Likelihood for Blind Source Separation
, 1997
"... Algorithms for the blind separation of sources can be derived from several different principles. This letter shows that the recently proposed infomax principle is equivalent to maximum likelihood. Introduction. Source separation consists in recovering a set of unobservable signals (sources) from a ..."
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Cited by 170 (2 self)
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Algorithms for the blind separation of sources can be derived from several different principles. This letter shows that the recently proposed infomax principle is equivalent to maximum likelihood. Introduction. Source separation consists in recovering a set of unobservable signals (sources) from a
Dispersal–vicariance analysis: a new approach to the quantification of historical biogeography
 SYST. BIOL
, 1997
"... Quantification in historical biogeography has usually been based on the search for a single branching relationship among areas of endemism. Unlike organisms, however, areas rarely have a unique hierarchical history. Dispersal barriers appear and disappear and may have different effects on different ..."
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Cited by 166 (4 self)
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on different species. As a result, the biota of an area may consist of several components with separate histories, each of which may be reticulate rather than branching. In an attempt to address these problems, I present a new biogeographic method, dispersalvicariance analysis, which reconstructs
Fast surface reconstruction using the level set method
 In VLSM ’01: Proceedings of the IEEE Workshop on Variational and Level Set Methods
, 2001
"... In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data ..."
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Cited by 151 (12 self)
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data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surfacelike model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling
Image Tag Refinement Towards LowRank, ContentTag Prior and Error Sparsity
"... The vast userprovided image tags on the popular photo sharing websites may greatly facilitate image retrieval and management. However, these tags are often imprecise and/or incomplete, resulting in unsatisfactory performances in tag related applications. In this work, the tag refinement problem is ..."
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Cited by 33 (3 self)
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is formulated as a decomposition of the userprovided tag matrix D into a lowrank refined matrix A and a sparse error matrix E, namelyD = A + E, targeting the optimality measured by four aspects: 1) lowrank: A is of lowrank owing to the semantic correlations among the tags; 2) content consistency: if two
Results 1  10
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