Non-negative tensor factorization with applications to statistics and computer vision
ICML '05 Proceedings of the 22nd international conference on Machine learning
Multidimensional filtering based on a tensor approach
Signal Processing
Survey on tensor signal algebraic filtering
Signal Processing
A Tensor Approximation Approach to Dimensionality Reduction
International Journal of Computer Vision
Sequential unfolding SVD for tensors with applications in array signal processing
IEEE Transactions on Signal Processing
Eigenvalues of a real supersymmetric tensor
Journal of Symbolic Computation
Learning concepts by modeling relationships
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
Journal of Global Optimization
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Common component analysis for multiple covariance matrices
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Alternating direction method for bi-quadratic programming
Journal of Global Optimization
Computers and Electrical Engineering
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
SIAM Journal on Scientific Computing
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
Gradient skewness tensors and local illumination detection for images
Journal of Computational and Applied Mathematics
A maximum enhancing higher-order tensor glyph
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Most Tensor Problems Are NP-Hard
Journal of the ACM (JACM)
Criterions for the positive definiteness of real supersymmetric tensors
Journal of Computational and Applied Mathematics
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Recently the problem of determining the best, in the least-squares sense, rank-1 approximation to a higher-order tensor was studied and an iterative method that extends the well-known power method for matrices was proposed for its solution. This higher-order power method is also proposed for the special but important class of supersymmetric tensors, with no change. A simplified version, adapted to the special structure of the supersymmetric problem, is deemed unreliable, as its convergence is not guaranteed. The aim of this paper is to show that a symmetric version of the above method converges under assumptions of convexity (or concavity) for the functional induced by the tensor in question, assumptions that are very often satisfied in practical applications. The use of this version entails significant savings in computational complexity as compared to the unconstrained higher-order power method. Furthermore, a novel method for initializing the iterative process is developed which has been observed to yield an estimate that lies closer to the global optimum than the initialization suggested before. Moreover, its proximity to the global optimum is a priori quantifiable. In the course of the analysis, some important properties that the supersymmetry of a tensor implies for its square matrix unfolding are also studied.