Non-negative tensor factorization with applications to statistics and computer vision
ICML '05 Proceedings of the 22nd international conference on Machine learning
Higher-Order Web Link Analysis Using Multilinear Algebra
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Generalized Low Rank Approximations of Matrices
Machine Learning
Multidimensional filtering based on a tensor approach
Signal Processing
Survey on tensor signal algebraic filtering
Signal Processing
Hierarchical Tensor Approximation of Multi-Dimensional Visual Data
IEEE Transactions on Visualization and Computer Graphics
Tensor-product approximation to operators and functions in high dimensions
Journal of Complexity
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
Journal of Computational Physics
Learning 3-D object orientation from images
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
MobiOpp '10 Proceedings of the Second International Workshop on Mobile Opportunistic Networking
Singular value decompositions and low rank approximations of tensors
IEEE Transactions on Signal Processing
Product form approximations for communicating Markov processes
Performance Evaluation
Journal of Computational and Applied Mathematics
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
Journal of Global Optimization
Recursive green's function registration
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
Fast track article: Connectivity in time-graphs
Pervasive and Mobile Computing
Quantum Information & Computation
Are tensor decomposition solutions unique? on the Global convergence HOSVD and parafac algorithms
PAKDD'11 Proceedings of the 15th Pacific-Asia conference on Advances in knowledge discovery and data mining - Volume Part I
Alternating direction method for bi-quadratic programming
Journal of Global Optimization
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
Array flattening based univariate high dimensional model representation (AFBUHDMR)
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
Dynamical Tensor Approximation
SIAM Journal on Matrix Analysis and Applications
On the computational benefit of tensor separation for high-dimensional discrete convolutions
Multidimensional Systems and Signal Processing
Modeling and multiway analysis of chatroom tensors
ISI'05 Proceedings of the 2005 IEEE international conference on Intelligence and Security Informatics
On the best rank-1 approximation to higher-order symmetric tensors
Mathematical and Computer Modelling: An International Journal
A New Truncation Strategy for the Higher-Order Singular Value Decomposition
SIAM Journal on Scientific Computing
Maximum Block Improvement and Polynomial Optimization
SIAM Journal on Optimization
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case
SIAM Journal on Scientific Computing
Tensor based sparse decomposition of 3D shape for visual detection of mirror symmetry
Computer Methods and Programs in Biomedicine
Robust tensor classifiers for color object recognition
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
A tensor factorization based least squares support tensor machine for classification
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
Criterions for the positive definiteness of real supersymmetric tensors
Journal of Computational and Applied Mathematics
An equi-directional generalization of adaptive cross approximation for higher-order tensors
Applied Numerical Mathematics
Tensor clustering via adaptive subspace iteration
Intelligent Data Analysis
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The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211--218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.