Exact minimum rank approximation via Schatten \(p\)-norm minimization

DOI10.1016/j.cam.2014.02.015zbMath1293.65056OpenAlexW2108165393MaRDI QIDQ396052

Wei Huang, Lu Liu, Di-Rong Chen

Publication date: 8 August 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.02.015

zbMATH Keywords

singular value decompositionrandom matrixSchatten \(p\)-normrank minimizationmajorization minimizationrestricted isometry constant

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Matrix completion problems (15A83)

Related Items (10)

Multiple kernel low-rank representation-based robust multi-view subspace clustering ⋮ Stable recovery of low-rank matrix via nonconvex Schatten \(p\)-minimization ⋮ Robust subspace clustering based on non-convex low-rank approximation and adaptive kernel ⋮ Multi-band weighted \(l_p\) norm minimization for image denoising ⋮ Recovery of low-rank matrices based on the rank null space properties ⋮ Proximal iteratively reweighted algorithm for low-rank matrix recovery ⋮ Robust image compressive sensing based on half-quadratic function and weighted Schatten-\(p\) norm ⋮ Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization ⋮ Convergence analysis of projected gradient descent for Schatten-\(p\) nonconvex matrix recovery ⋮ Optimal RIP bounds for sparse signals recovery via \(\ell_p\) minimization

Uses Software

• softImpute
• ADMiRA

Cites Work

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• Estimation of high-dimensional low-rank matrices
• Weighted minimum trace factor analysis
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• Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• On the rank minimization problem over a positive semidefinite linear matrix inequality
• ADMiRA: Atomic Decomposition for Minimum Rank Approximation
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
• Stable signal recovery from incomplete and inaccurate measurements

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