An efficient randomized algorithm for computing the approximate Tucker decomposition
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Publication:2049079
DOI10.1007/s10915-021-01545-5OpenAlexW3175303573MaRDI QIDQ2049079
Hong Yan, Mao-Lin Che, Yi-Min Wei
Publication date: 24 August 2021
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-021-01545-5
randomized algorithmsrandom projectionapproximate Tucker decompositiondimension reduction mapspower iteration techniquesubsampled randomized Fourier transformthin QR decomposition
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Randomized algorithms (68W20)
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Cites Work
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Tensor Decompositions and Applications
- Handwritten digit classification using higher order singular value decomposition
- A randomized algorithm for a tensor-based generalization of the singular value decomposition
- A fast randomized algorithm for the approximation of matrices
- Randomized LU decomposition using sparse projections
- Randomized algorithms for the low multilinear rank approximations of tensors
- Smallest singular value of random matrices and geometry of random polytopes
- Randomized algorithms for the approximations of Tucker and the tensor train decompositions
- Randomized Alternating Least Squares for Canonical Tensor Decompositions: Application to A PDE With Random Data
- A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices
- A literature survey of low-rank tensor approximation techniques
- Improved Matrix Algorithms via the Subsampled Randomized Hadamard Transform
- Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case
- A New Truncation Strategy for the Higher-Order Singular Value Decomposition
- Computational Advertising: Techniques for Targeting Relevant Ads
- Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme
- Randomized Algorithms for Matrices and Data
- Low-Rank Approximation and Regression in Input Sparsity Time
- Algorithm 862
- A Newton–Grassmann Method for Computing the Best Multilinear Rank-$(r_1,$ $r_2,$ $r_3)$ Approximation of a Tensor
- A Multilinear Singular Value Decomposition
- On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
- A randomized tensor singular value decomposition based on the t‐product
- Practical Sketching Algorithms for Low-Rank Matrix Approximation
- Hankel Matrix Nuclear Norm Regularized Tensor Completion for $N$-dimensional Exponential Signals
- Randomized Algorithms for Low-Rank Tensor Decompositions in the Tucker Format
- Low-Rank Tucker Approximation of a Tensor from Streaming Data
- The Computation of Low Multilinear Rank Approximations of Tensors via Power Scheme and Random Projection
- The Fast Johnson–Lindenstrauss Transform and Approximate Nearest Neighbors
- Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
- Theory and Computation of Complex Tensors and its Applications
- Universality laws for randomized dimension reduction, with applications
- Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
- Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix