Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Matrix computations (3rd ed.)
Bibliography on higher-order statistics
Signal Processing
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
Trust-region methods
Algorithms for Numerical Analysis in High Dimensions
SIAM Journal on Scientific Computing
Tensor-based techniques for the blind separation of DS-CDMA signals
Signal Processing
Trust-Region Methods on Riemannian Manifolds
Foundations of Computational Mathematics
Computational Intelligence and Neuroscience - EEG/MEG Signal Processing
Multiway analysis of epilepsy tensors
Bioinformatics
Fast Multilinear Singular Value Decomposition for Structured Tensors
SIAM Journal on Matrix Analysis and Applications
Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions
SIAM Journal on Matrix Analysis and Applications
Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
SIAM Journal on Matrix Analysis and Applications
A geometric newton method for oja's vector field
Neural Computation
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
SIAM Journal on Matrix Analysis and Applications
Tensor Decompositions and Applications
SIAM Review
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
SIAM Journal on Scientific Computing
IEEE Transactions on Signal Processing - Part II
Blind PARAFAC receivers for DS-CDMA systems
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
Online learning in the embedded manifold of low-rank matrices
The Journal of Machine Learning Research
A New Truncation Strategy for the Higher-Order Singular Value Decomposition
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
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Higher-order tensors are used in many application fields, such as statistics, signal processing, and scientific computing. Efficient and reliable algorithms for manipulating these multi-way arrays are thus required. In this paper, we focus on the best rank-$(R_1,R_2,R_3)$ approximation of third-order tensors. We propose a new iterative algorithm based on the trust-region scheme. The tensor approximation problem is expressed as a minimization of a cost function on a product of three Grassmann manifolds. We apply the Riemannian trust-region scheme, using the truncated conjugate-gradient method for solving the trust-region subproblem. Making use of second order information of the cost function, superlinear convergence is achieved. If the stopping criterion of the subproblem is chosen adequately, the local convergence rate is quadratic. We compare this new method with the well-known higher-order orthogonal iteration method and discuss the advantages over Newton-type methods.