Literature survey on low rank approximation of matrices
From MaRDI portal
Publication:4603753
DOI10.1080/03081087.2016.1267104zbMath1387.65039arXiv1606.06511OpenAlexW2963450965MaRDI QIDQ4603753
N. Kishore Kumar, Jan Schneider
Publication date: 19 February 2018
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.06511
complexitysingular value decompositionsubset selectionFrobenius normrankrandomized algorithmpseudoinverseQR decompositionsubsamplingrandom projectionspectral normadaptive cross approximationpivotpseudoskeleton approximationmaximal volumeinterpolative decompositioncross/skeleton decomposition
Related Items
CDPA: common and distinctive pattern analysis between high-dimensional datasets ⋮ A strengthened Barvinok-Pataki bound on SDP rank ⋮ CMD: controllable matrix decomposition with global optimization for deep neural network compression ⋮ Seq-SVF: an unsupervised data-driven method for automatically identifying hidden governing equations ⋮ A literature survey of matrix methods for data science ⋮ Inexact penalty decomposition methods for optimization problems with geometric constraints ⋮ Polynomial whitening for high-dimensional data ⋮ Parallel cross interpolation for high-precision calculation of high-dimensional integrals ⋮ Imputation and low-rank estimation with missing not at random data ⋮ Column subset selection is NP-complete ⋮ Randomized recompression of \(\mathcal {H}\)-matrices for BEM ⋮ Least upper bound of truncation error of low-rank matrix approximation algorithm using QR decomposition with pivoting ⋮ Analytical Low-Rank Compression via Proxy Point Selection ⋮ On the rank-one approximation of positive matrices using tropical optimization methods ⋮ Linear-time CUR approximation of BEM matrices ⋮ Main effects and interactions in mixed and incomplete data frames ⋮ Interpolative Decomposition via Proxy Points for Kernel Matrices ⋮ A Multiscale Neural Network Based on Hierarchical Matrices ⋮ Bivariate Hermite interpolation by a limiting case of the cross approximation algorithm ⋮ Best Low-rank Approximations and Kolmogorov $n$-widths ⋮ Sublinear Cost Low Rank Approximation via Subspace Sampling ⋮ An ensemble of high rank matrices arising from tournaments
Uses Software
Cites Work
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- TT-cross approximation for multidimensional arrays
- CUR matrix decompositions for improved data analysis
- Generalized cross approximation for 3D-tensors
- A note on tensor chain approximation
- Rang revealing QR factorizations
- Error estimates for two-dimensional cross approximation
- A randomized algorithm for the decomposition of matrices
- Quasioptimality of skeleton approximation of a matrix in the Chebyshev norm
- Randomized SVD methods in hyperspectral imaging
- Adaptive cross approximation of multivariate functions
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- Column subset selection via sparse approximation of SVD
- A robust and efficient parallel SVD solver based on restarted Lanczos bidiagonalization
- Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
- A fast randomized algorithm for the approximation of matrices
- Generalizing the column-row matrix decomposition to multi-way arrays
- Algorithms and applications for approximate nonnegative matrix factorization
- On selecting a maximum volume sub-matrix of a matrix and related problems
- Approximation theory in tensor product spaces
- Rank and null space calculations using matrix decomposition without column interchanges
- Pseudo-skeleton approximations by matrices of maximal volume
- A theory of pseudoskeleton approximations
- Pseudoskeleton approximations of matrices
- Adaptive low-rank approximation of collocation matrices
- Incomplete cross approximation in the mosaic-skeleton method
- Approximation of boundary element matrices
- Latent semantic indexing: A probabilistic analysis
- Four algorithms for the the efficient computation of truncated pivoted QR approximations to a sparse matrix
- Principal component analysis.
- Randomized algorithms for low-rank matrix factorizations: sharp performance bounds
- The fast solution of boundary integral equations.
- A fast block low-rank dense solver with applications to finite-element matrices
- Hybrid regularization for MRI reconstruction with static field inhomogeneity correction
- Handbook series linear algebra. Linear least squares solutions by Householder transformations
- Matrix Algorithms
- Frequent Directions: Simple and Deterministic Matrix Sketching
- A literature survey of low-rank tensor approximation techniques
- Regularization with randomized SVD for large-scale discrete inverse problems
- Sublinear Randomized Algorithms for Skeleton Decompositions
- Randomized algorithms for the low-rank approximation of matrices
- Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons
- Randomized Algorithms for Matrices and Data
- Fast low rank approximations of matrices and tensors
- Extensions of Lipschitz mappings into a Hilbert space
- Verification of the cross 3D algorithm on quantum chemistry data
- Fast computation of low-rank matrix approximations
- Sampling from large matrices
- Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
- A Randomized Algorithm for Principal Component Analysis
- Adaptive Sampling and Fast Low-Rank Matrix Approximation
- Subspace Sampling and Relative-Error Matrix Approximation: Column-Based Methods
- Hierarchische Matrizen
- Relative-Error $CUR$ Matrix Decompositions
- Spectral Algorithms
- Rank-Revealing QR Factorizations and the Singular Value Decomposition
- Some Applications of the Rank Revealing QR Factorization
- On Rank-Revealing Factorisations
- A Multilinear Singular Value Decomposition
- Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications
- Quasi-Polynomial Time Approximation Scheme for Sparse Subsets of Polygons
- An elementary proof of a theorem of Johnson and Lindenstrauss
- Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
- On Tensors, Sparsity, and Nonnegative Factorizations
- Numerical linear algebra in the streaming model
- A fast and efficient algorithm for low-rank approximation of a matrix
- Subspace Iteration Randomization and Singular Value Problems
- On the Compression of Low Rank Matrices
- Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
- Learning the parts of objects by non-negative matrix factorization
- Tighter Low-rank Approximation via Sampling the Leveraged Element
- Fast monte-carlo algorithms for finding low-rank approximations
- Projected Gradient Methods for Nonnegative Matrix Factorization
- Algorithm 844
- Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
- Fast Monte Carlo Algorithms for Matrices III: Computing a Compressed Approximate Matrix Decomposition
- Near Optimal Column-Based Matrix Reconstruction
- Optimal Column-Based Low-Rank Matrix Reconstruction
- Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications
- Generalized low rank approximations of matrices
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
