RTRMC: A Riemannian trust-region method for low-rank matrix completion

By Nicolas Boumal, Pierre-Antoine Absil. 2011

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Examples include nonlinear conjugate gradient or Newton-like methods on manifolds of low-rank matrices [35,191,198,257,258] or low-rank tensors [52,53,131,132,255], see also Section 3.4.”
Recent advances in trust region algorithms (2015, methodology): “Recently, a Riemannian trust region method for low-rank matrix completion is given by Boumal and Absil [8], which studies the problem of recovering large scale low-rank matrices when most of the entries are unknown.”
Scaled Gradients on Grassmann Manifolds for Matrix Completion (2012, methodology): “In terms of iteration counts, we can see that for the fully random case (upper row), RTRMC2 is the best while ScGrass-CG and Riemann-CG converger asonably fast.”
Exact Tensor Completion Using t-SVD (2015, background): “Recovery of tensors under limited number of measurements is an important problem, which arises in a variety of applications, such as recommendation systems [4], dimensionality reduction [5], multi-class learning [6],data mining [7], [8] and computer vision [9], [2].”
Manopt, a matlab toolbox for optimization on manifolds (2013, background): “…the Grassmann manifold proves useful in low-rank matrix completion, where it is observed that if one knows the column space spanned by the sought matrix, then completing the matrix according to a least squares criterion is easy (Keshavan et al. , 2010; Boumal & Absil, 2011; Balzano et al. , 2010).”
Low-Rank Matrix Completion by Riemannian Optimization (2012, methodology): “Analogous modifications also appear in [8, 9, 28].”
Tensor Factorization for Low-Rank Tensor Completion (2018, unknown): “Besides, by directly restricting the rank of the estimation, the low-rank factorization methods can also well recover the low-rank data and achieve stateof-the-art completion results in image/video inpainting [25], [27], [28], and collaborative filtering [26], [29].”