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

By Zaiwen Wen, Wotao Yin, Yin Zhang. Mathematical Programming Computation, 2012

824 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/4a3d4c584e184947a6f235366160cc78979d7fa1

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In Aerospace Engineering

In Computational Mechanics

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Citations in the corpus

Stability of matrix factorization for collaborative filtering (2012, neutral): “As documented in Mitra et al. (2010); Wen (2010) and many others, matrix factorization methods typically outperform these two methods.”
Tensor Factorization for Low-Rank Tensor Completion (2018, methodology): “Similar to [3] and [25], we adopt the rankdecreasing method to estimate the true rank of a tensor.”
On critical points of quadratic low-rank matrix optimization problems (2020, background): “Solvers for these problems with the best theoretical guarantees are based on convex relaxation [9, 10], but they can also be treated well by local optimization techniques [40, 37]”
Parallel stochastic gradient algorithms for large-scale matrix completion (2013, neutral): “[41].”
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train (2016, methodology): “This model is similar to the one proposed in [20], [21] (which is an extension of the matrix completion model [44]) where the Tucker rank is employed.”
A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update (2014, background): “Numerically, [35,58] demonstrate that extrapolation technique can also accelerate algorithms for nonconvex matrix factorization problems.”
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, background): “This UV - parametrization approach is capable of avoiding the computation of SVD (see, e.g., [54]), and it beneﬁts from the reduction of dimensionality from mn to ( m + n ) r (normally, r min( m, n ) for optimization problems with the low-rank concern).”
Group sparse optimization by alternating direction method (2013, methodology): “where ri := xgi + 1 β1 (λ1)gi , (13) and the convention 0 · 0 0 = 0 is followed.”
Efficient matrix completion for seismic data reconstruction (2015, methodology): “We used Jellyfish and SPG-LR implementations to complete the resulting incomplete matrix and compared these methods to the ADMM Tensor method and LMaFit, an alternating least-squares approach to matrix completion detailed in Wen et al. (2012).”
Generalized Nonconvex Nonsmooth Low-Rank Minimization (2014, background): “[22] and Truncated Nuclear Norm Regularization (TNNR) [16].”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “As is now well known, 1-norm minimization has been used to recover sparse signals in compressive sensing [5,6,9,14], and nuclear-norm minimization has been used to recover a low-rank matrix from a subset of its entries in matrix completion [3,43].”
Distributed optimization for multi-task learning via nuclear-norm approximation (2015, methodology): “…use techniques such as approximate singular value decompositions (Woolfe et al., 2008; Witten and Candès, 2015); coordinate descent and subspace selection (Dud́ık et al., 2012; Hsieh and Olsen, 2014); and successive over-relaxation (Wen et al., 2012), which is again related to coordinate descent.”
Guaranteed Matrix Completion via Non-Convex Factorization (2014, background): “Index Terms —Matrix completion, matrix factorization, nonconvex optimization, alternating minimization, SGD, perturbation analysis.”