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
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Efficient MATLAB Computations with Sparse and Factored Tensors
SIAM Journal on Scientific Computing
Enhanced Line Search: A Novel Method to Accelerate PARAFAC
SIAM Journal on Matrix Analysis and Applications
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Tensor Decompositions and Applications
SIAM Review
Multi-way space-time-wave-vector analysis for EEG source separation
Signal Processing
An analytical constant modulus algorithm
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part II
Blind spatial signature estimation via time-varying user power loading and parallel factor analysis
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Robust iterative fitting of multilinear models
IEEE Transactions on Signal Processing - Part I
A Tensor Framework for Nonunitary Joint Block Diagonalization
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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In this paper, we propose a framework to compute approximate CANDECOMP / PARAFAC (CP) decompositions. Such tensor decompositions are viable tools in a broad range of applications, creating the need for versatile tools to compute such decompositions with an adjustable complexity-accuracy trade-off. To this end, we propose a novel SEmi-algebraic framework that allows the computation of approximate C P decompositions via SImultaneous Matrix Diagonalizations (SECSI). In contrast to previous Simultaneous Matrix Diagonalization (SMD)-based approaches, we use the tensor structure to construct not only one but the full set of possible SMDs. Solving all SMDs, we obtain multiple estimates of the factor matrices and present strategies to choose the best estimate in a subsequent step. This SECSI framework retains the option to choose the number of SMDs to solve and to adopt various strategies for the selection of the final solution out of the multiple estimates. A best matching scheme based on an exhaustive search as well as heuristic selection schemes are devised to flexibly adapt to specific applications. Four example algorithms with different accuracy-complexity trade-off points are compared to state-of-the-art algorithms. We obtain more reliable estimates and a reduced computational complexity.