Low-rank tensor completion by Riemannian optimization

By Daniel Kressner, Michael Steinlechner, Bart Vandereycken. 2014

344 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/080db220ddd6929101d16e82e9a17c079436ad14

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Citations in the corpus

A Unified Perspective on Multi-Domain and Multi-Task Learning (2014, methodology): “ZSDA can be formalised by setting the model parameters for the held-out domain to missing values, and recovering them by a low-rank tensor completion algorithm (Kressner et al., 2014).”
Parallel matrix factorization for low-rank tensor completion (2013, unknown): “The work [12] directly constrains the solution in some low-rank manifold and employs the Riemannian optimization to solve the problem.”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, background): “While algorithms for this purpose are available both for low rank and low multilinear rank representation [59,87,88], an even more drastic approach would be to directly adopt sampled fibers as the bases in a tensor representation.”
Rubik: Knowledge Guided Tensor Factorization and Completion for Health Data Analytics (2015, background): “A number of other alternatives have also been discussed in [20, 24, 28].”
Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination (2014, methodology): “Some other related methods were also investigated such as structured CPD using nonlinear least squares (CPNLS) [11] and geometric nonlinear conjugate gradient (geomCG) [12].”
Manopt, a matlab toolbox for optimization on manifolds (2013, background): “All the manifolds mentioned in the introduction work out of the box, and more can be added (shape space (Ring & Wirth, 2012), low-rank tensors (Kressner et al. , 2013), etc.).”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “…to eﬃciently parameterize, through structured compact representations, very general high-dimensional spaces which arise in modern applications (Kressner et al. , 2014b; Cichocki, 2014; Zhang et al. , 2015; Corona et al. , 2015; Litsarev and Oseledets, 2016; Khoromskij and Veit, 2016; Benner…”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “…are right-orthogonal G(p) (1) G (p) T (1) = G (p) ă1ą G (p) T ă1ą = IRp´1 , p ą n, (3.14) then the frame matrices have orthogonal columns [Dolgov et al., 2014, Kressner et al., 2014a, Pižorn and Verstraete, 2012], that is GT‰ n G‰ n = IRn´1 In Rn , (3.15) GT‰ n,n+1 G‰ n,n+1 = IRn´1 In In+1 Rn+1 .”
Exact Tensor Completion Using t-SVD (2015, methodology): “…is the Low Rank Tensor Completion(LRTC) algorithm in [9], the third one is the tensor completion in Tucker format by Riemannian optimization [33], the fourth approach is our tensor completion with random sampling via t-SVD, and the last approach is tensor completion with tubal sampling[31]…”