PARAFAC: parallel factor analysis
Computational Statistics & Data Analysis - Special issue on multiway data analysis—software and applications
Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Decomposition of quantics in sums of powers of linear forms
Signal Processing - Special issue on higher order statistics
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
Blind identification of under-determined mixtures based on the characteristic function
Signal Processing - Signal processing in UWB communications
SIAM Journal on Matrix Analysis and Applications
Enhanced Line Search: A Novel Method to Accelerate PARAFAC
SIAM Journal on Matrix Analysis and Applications
A comparison of algorithms for fitting the PARAFAC model
Computational Statistics & Data Analysis
Fourth-order blind identification of underdetermined mixtures of sources (FOBIUM)
IEEE Transactions on Signal Processing
Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Parallel factor analysis in sensor array processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Frequency domain blind MIMO system identification based on second and higher order statistics
IEEE Transactions on Signal Processing
Hi-index | 0.08 |
Two main drawbacks can be stated in the alternating least square (ALS) algorithm used to fit the canonical decomposition (CAND) of multi-way arrays. First its slow convergence caused by the presence of collinearity between factors in the multi-way array it decomposes. Second its blindness to Hermitian symmetries of the considered arrays. Enhanced line search (ELS) scheme was found to be a good way to cope with the slow convergence of the ALS algorithm together with a partial use of the Hermitian symmetry. However, to our knowledge, required equations to perform the latter scheme are only given in the case of third and fifth order arrays. Therefore, our first contribution consists in generalizing the ELS procedure to the case of complex arrays of any order greater than three. Our second contribution is another improvement of the ALS scheme, able to profit from Hermitianity and positive semi-definiteness of the considered arrays. It consists in resorting to the CAND first of a third order array having one unitary loading matrix and second of several rank-1 arrays. An iterative algorithm is then proposed alternating between Procrustes problem solving and the computation of rank-one matrix approximations in order to achieve the CAND of the third order array.