Tensor completion and low-n-rank tensor recovery via convex optimization

By Silvia Gandy, B. Recht, Isao Yamada. 2011

838 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “In this respect, this situation is quite different from the growing area of tensor completion, see, e.g., [92,182], where the selection of the entries is usually prescribed by the application.”
Parallel matrix factorization for low-rank tensor completion (2013, neutral): “Existingmethods for LRTC in [16, 3] employ matrix nuclear-norm minimization and use the singular value decomposition (SVD) in their algorithms, which become very slow or even not applicable for large-scale problems.”
Tensor Factorization for Low-Rank Tensor Completion (2018, background): “Recent research [2], [3], [6], [7], [10]–[13] shows that high dimensional tensor data of interest, such as videos and image collections, are usually intrinsically low-rank or approximately so.”
Nonsingular $H$-tensor and its criteria (2016, background): “Hence, tensor analysis and computing have received much attention of researchers in recent decade and the research branches include spectral hypergraph theory [13, 29], best low-rank approximation to tensors [15, 17, 37], positive definiteness identification of even order homogenous polynomials [12,”
Efficient matrix completion for seismic data reconstruction (2015, methodology): “Large scale tensor completion Following the approach of Kreimer et al. (2013), which applies the method developed in Gandy et al. (2011) to seismic data, we can also exploit the tensor structure of a frequency slice F for interpolating missing traces.”
Exact Tensor Completion Using t-SVD (2015, methodology): “Approaches based on Tucker decomposition work by unfolding the tensor in various ways, subsequently employing the theory and methods for matrix completion, see for example [15], [16].”
Multi-Task Feature Interaction Learning (2016, methodology): “One way is to use the average rank of unfolding on different mode [15]:”
Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination (2014, methodology): “To improve the efficiency, Douglas-Rachford splitting technique [16], nonlinear Gauss-Seidal method [17] were also investigated.”
A Survey of Deep Learning-Based Object Detection (2019, neutral): “structure detection, researches propose strong baseline in both 2D images [192] [193] and 3D point clouds [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205].”
Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography (2013, methodology): “For the first approach, we are motivated by [21], [22], and [34] where the idea of matrix completion via nuclear norm minimization is generalized to the tensor case using the matricization (unfolding) operation.”
RadioUNet: Fast Radio Map Estimation With Convolutional Neural Networks (2019, background): “The dominating term in each iteration is due to SVD within the shrinkage operation [61].”
Multilinear Multitask Learning (2013, methodology): “This solution is based on several recent studies which have showed that the use of the trace norm of tensors provides close convex approximations of similar minimization problems (Gandy et al., 2011; Liu et al., 2009; Signoretto et al., 2011; Tomioka, 2010).”