Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm

Wen, Zaiwen; Yin, Wotao; Zhang, Yin

doi:10.1007/s12532-012-0044-1

Cited by 697 publications

(602 citation statements)

References 27 publications

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“…In this sense, if the algorithm has converged, we can a posteriori use the boundedness of the sequence to show that the limit point is a local stationary point. This is a slightly different guarantee than that proved in [20].…”

Section: Proximal Gradient Methodsmentioning

confidence: 73%

Metric learning with rank and sparsity constraints

Bah

Becker

Cevher

et al. 2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Choosing a distance preserving measure or metric is fundamental to many signal processing algorithms, such as kmeans, nearest neighbor searches, hashing, and compressive sensing. In virtually all these applications, the efficiency of the signal processing algorithm depends on how fast we can evaluate the learned metric. Moreover, storing the chosen metric can create space bottlenecks in high dimensional signal processing problems. As a result, we consider data dependent metric learning with rank as well as sparsity constraints. We propose a new non-convex algorithm and empirically demonstrate its performance on various datasets; a side benefit is that it is also much faster than existing approaches. The added sparsity constraints significantly improve the speed of multiplying with the learned metrics without sacrificing their quality.

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Section: Proximal Gradient Methodsmentioning

confidence: 73%

Metric learning with rank and sparsity constraints

Bah

Becker

Cevher

et al. 2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…We compared our algorithm in [9] with LMaFit [11] and FPCA [12] on recovering three-dimensional hyperspectral images from their incomplete observations. Our test hyperspectral datacube has 163 slices, and the size of each slice is 80 × 80.…”

Section: Numerical Resultsmentioning

confidence: 99%

Compressive Hyperspectral Imaging and Anomaly Detection

Thiyanarantnam¹,

Osher²,

Chen³

et al. 2013

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“…A further saving is achieved in the "LMaFit" algorithm proposed by Wen et al [277]. Here the basic Proximal-ALS iteration is carried out with only one QR factorization which is used to generate an orthonormal basis to the column space of the matrix A ℓ V ℓ .…”

Section: The Lmafit Algorithmmentioning

confidence: 99%

“…Otherwise, when the columns of V ℓ are linearly dependent, the proof is concluded by using the SVD of V ℓ , see [277].…”

Section: The Lmafit Algorithmmentioning

confidence: 99%

Imputing Missing Entries of a Data Matrix: A Review

Dax¹

2014

JAC

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The problem of imputing missing entries of a data matrix is easy to state: Some entries of the matrix are unknown and we want to assign "appropriate values" to these entries. The need for solving such problems arises in several applications, ranging from traditional ields to modern ones. Typical examples of traditional ields are statistical analysis of incomplete survey data, business reports, operations management, psychometrika, meteorology and hydrology. Modern applications arise in machine learning, data mining, DNA microarrays data, chemometrics, computer vision, recommender systems and collaborative iltering. The problem is highly interesting and challenging. Many ingenious algorithms have been proposed, and there is vast literature on imputing techniques. Yet, most of the papers consider the imputing problem within the context of a speci ic application or a speci ic approach. The current survey provides a broad view of the problem, one that exposes the large variety of imputing methods. Old and new methods are examined with focus on the ideas behind the methods. It is illustrated how simple ideas evolve into highly sophisticated algorithms. The review enables us to identify a number of basic concepts and tools which are shared by several imputing methods. Equivalence theorems that we prove reveal surprising relations between apparently different methods.

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Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm

Cited by 697 publications

References 27 publications

Metric learning with rank and sparsity constraints

Metric learning with rank and sparsity constraints

Compressive Hyperspectral Imaging and Anomaly Detection

Imputing Missing Entries of a Data Matrix: A Review

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