Matrix computations (3rd ed.)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Orthogonal Tensor Decompositions
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Convex Optimization
Multilinear Independent Components Analysis
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
ACM Transactions on Mathematical Software (TOMS)
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
On the Tensor SVD and the Optimal Low Rank Orthogonal Approximation of Tensors
SIAM Journal on Matrix Analysis and Applications
Higher Order SVD Analysis for Dynamic Texture Synthesis
IEEE Transactions on Image Processing
A tensor decomposition approach to data compression and approximation of ND systems
Multidimensional Systems and Signal Processing
Joint image denoising using adaptive principal component analysis and self-similarity
Information Sciences: an International Journal
Hi-index | 35.68 |
The singular value decomposition is among the most important tools in numerical analysis for solving a wide scope of approximation problems in signal processing, model reduction, system identification and data compression. Nevertheless, there is no straightforward generalization of the algebraic concepts underlying the classical singular values and singular value decompositions to multilinear functions. Motivated by the problem of lower rank approximations of tensors, this paper develops a notion of singular values for arbitrary multilinear mappings. We provide bounds on the error between a tensor and its optimal lower rank approximation. Conceptual algorithms are proposed to compute singular value decompositions of tensors.