Robust CUR Decomposition: Theory and Imaging Applications

DOI10.1137/20M1388322MaRDI QIDQ5860372

Deanna Needell, HanQin Cai, Longxiu Huang, Keaton Hamm

Publication date: 19 November 2021

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.05231

zbMATH Keywords

robust algorithmslow-rank matrix approximationCUR decompositionRPCAinterpolative decompositionsrobust CUR

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Information storage and retrieval of data (68P20) Approximation algorithms (68W25) Randomized algorithms (68W20)

Related Items

Coseparable Nonnegative Matrix Factorization, Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion, CUR and Generalized CUR Decompositions of Quaternion Matrices and their Applications, Generalized pseudoskeleton decompositions

Cites Work

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• TT-cross approximation for multidimensional arrays
• CUR matrix decompositions for improved data analysis
• Similarity matrix framework for data from union of subspaces
• Pseudo-skeleton approximations by matrices of maximal volume
• A theory of pseudoskeleton approximations
• Pseudo-skeleton approximations with better accuracy estimates
• Rectangular maximum-volume submatrices and their applications
• A good submatrix is hard to find
• Column subset selection is NP-complete
• Perspectives on CUR decompositions
• Efficient algorithms for CUR and interpolative matrix decompositions
• Column subset selection problem is UG-hard
• A DEIM Induced CUR Factorization
• Sublinear Randomized Algorithms for Skeleton Decompositions
• Optimal CUR Matrix Decompositions
• Robust principal component analysis?
• Rank-Sparsity Incoherence for Matrix Decomposition
• IMPROVED ANALYSIS OF THE SUBSAMPLED RANDOMIZED HADAMARD TRANSFORM
• Relative-Error $CUR$ Matrix Decompositions
• On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
• Accelerated Alternating Projections for Robust Principal Component Analysis
• Column Subset Selection, Matrix Factorization, and Eigenvalue Optimization
• Downdating the Singular Value Decomposition
• Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery
• Robust PCA via Outlier Pursuit
• Faster Subset Selection for Matrices and Applications
• Fast Monte Carlo Algorithms for Matrices III: Computing a Compressed Approximate Matrix Decomposition
• Near-Optimal Column-Based Matrix Reconstruction
• Perturbations of CUR Decompositions