Tensor decompositionsstate of the art and applications, keynote address in ima conf, Mathematics in Signal Processing ,
The expression of a tensor or a polyadic as a sum of products, J. Math. and Phys, vol.6, issue.1, pp.165-189, 1927. ,
Foundations of the parafac procedure: Models and conditions for an" explanatory" multimodal factor analysis ,
Determination and proof of minimum uniqueness condi-380 tions for parafac1, UCLA Working Papers in phonetics, vol.22, p.3, 1972. ,
Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition, Psychometrika, vol.35, issue.3, pp.283-319, 1970. ,
Towards a standardized notation and terminology in multiway analysis, J. Chemometrics, vol.14, pp.105-122, 2000. ,
Tensor decompositions, alternating least squares and other tales, Journal of Chemometrics: A Journal of the Chemometrics Society, vol.23, issue.7-8, pp.393-405, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00410057
, Parafac. tutorial and applications, Chemometrics and intelligent laboratory systems, vol.38, pp.149-171, 1997.
URL : https://hal.archives-ouvertes.fr/hal-02141162
Fluorescence spectroscopy and multi-way techniques. parafac, Analytical Methods, vol.5, issue.23, pp.6557-6566, 2013. ,
Blind separation of sources, part i: An adaptive algorithm based on neuromimetic architecture, Signal processing, vol.24, issue.1, pp.1-10, 1991. ,
Cp decomposition approach to blind separation for ds-cdma system using a new performance 400 index, EURASIP Journal on Advances in Signal Processing, vol.2014, issue.1, p.128, 2014. ,
Blind parafac receivers for ds-cdma systems, IEEE Transactions on Signal Processing, vol.48, issue.3, 2000. ,
Joint source estimation and localization, IEEE Transactions on Signal Processing, vol.63, issue.10, pp.2485-2495, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01005352
Denoising of hyperspectral images using the parafac model and statistical performance analysis, IEEE Transactions on Geoscience and Remote Sensing, vol.50, issue.10, pp.3717-3724, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01280605
Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear algebra and its applications, vol.18, issue.2, pp.95-138, 1977. ,
On kruskals uniqueness condition for the candecomp/parafac decomposition, Linear Algebra and its applications, vol.415, issue.420, pp.540-552, 2007. ,
Some mathematical notes on three-mode factor analysis, Psychometrika, vol.31, issue.3, pp.279-311, 1966. ,
Cf van loan, matrix computations ,
How 3-mfa data can cause degenerate 420 parafac solutions, among other relationships, Multiway data analysis, pp.115-122, 1989. ,
Enhanced line search: A novel method to accelerate parafac, SIAM journal on matrix analysis and applications, vol.30, issue.3, pp.1128-1147, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00327595
Slowly converging parafac sequences: swamps and two-factor degeneracies, Journal of Chemometrics, vol.8, issue.2, pp.155-168, 1994. ,
Two-factor degeneracies and a stabilization of parafac, Chemometrics and Intelligent Laboratory Systems, vol.38, issue.2, pp.173-181, 1997. ,
The problem and nature of degenerate solutions or decompositions of 3-way arrays, Talk at the Tensor Decompositions Workshop, 2004. ,
Construction and analysis of degenerate parafac models, Journal of Chemometrics: A Journal of the Chemometrics Society, vol.14, issue.3, 2000. ,
Some convergence results on the regularized alternating least-squares method for tensor decomposition, Lin. Algebra Appl, vol.438, issue.2, pp.796-812, 2013. ,
Tensorial resolution: a direct trilinear decom-440 position, Journal of Chemometrics, vol.4, issue.1, pp.29-45, 1990. ,
A decomposition for three-way arrays, SIAM Journal on Matrix Analysis and Applications, vol.14, issue.4, pp.1064-1083, 1993. ,
A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization, SIAM journal on, p.445 ,
, Matrix Analysis and Applications, vol.28, issue.3, pp.642-666, 2006.
Improving the speed of multi-way algorithms:: Part i. tucker3, Chemometrics and intelligent laboratory systems, vol.42, pp.93-103, 1998. ,
Improving the speed of multiway algorithms: Part 450 ii: Compression, Chemometrics and intelligent laboratory systems, vol.42, pp.105-113, 1998. ,
Enhanced line search : A novel method to accelerate Parafac, SIAM Journal on Matrix Analysis Appl, vol.30, issue.3, pp.1148-1171, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00327595
Robust independent component analysis, IEEE Trans. Neural Networks, vol.21, issue.2, pp.248-261, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00457300
, Coherence constrained 460 alternating least squares, pp.613-617, 2018.
, Proximal algorithms, vol.1, pp.127-239, 2014.
Proximal splitting methods in signal pro-465 cessing, in: Fixed-point algorithms for inverse problems in science and engineering, pp.185-212, 2011. ,
Ranks of tensors, secant varieties of Segre varieties and fat points, Linear Algebra Appl, vol.355, pp.263-285, 2002. ,
Tensor rank and the ill-posedness of the best low-rank approximation problem, SIAM Journal on Matrix Analysis Appl, vol.30, issue.3, pp.1084-1127, 2008. ,
Tensors: a brief introduction, IEEE Signal Processing Magazine, vol.31, issue.3, pp.44-53, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00923279
Tensor decompositions and applications, SIAM review, vol.51, issue.3, pp.455-500, 2009. ,
Optimally sparse representation in general (nonorthogonal) dictionaries via 1 minimization, Proceedings of the National Academy of Sciences, vol.100, issue.5, pp.2197-2202, 2003. ,
Sparsity and incoherence in compressive sampling, Inverse problems, vol.23, issue.3, p.969, 2007. ,
, The power of convex relaxation: Near-optimal matrix completion
, Sparse representations in unions of bases, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00570057
On the uniqueness of the canonical polyadic decomposition of third-order tensors-part i: Basic results and uniqueness of one factor matrix, SIAM Journal on Matrix Analysis and Applications, vol.34, issue.3, pp.855-875, 2013. ,
Blind multilinear identification, IEEE Transactions on Information Theory, vol.60, issue.2, pp.1260-1280, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00763275
Interior methods for constrained optimization, Acta numerica, vol.1, pp.341-407, 1992. ,
Interior point methods 25 years later, European Journal of 495 Operational Research, vol.218, issue.3, pp.587-601, 2012. ,
Applying gradient projection and conjugate gradient to the optimum operation of reservoirs 1, JAWRA Journal of the American Water Resources Association, vol.6, issue.5, pp.713-724, 1970. ,
Global convergence of a modified fletcher-reeves 500 conjugate gradient method with armijo-type line search, Numerische Mathematik, vol.104, issue.4, pp.561-572, 2006. ,
A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM journal on imaging sciences, vol.2, issue.1, pp.183-202, 2009. ,
A comparison of algorithms for fitting the parafac model, Computational Statistics & Data Analysis, vol.50, issue.7, pp.1700-1734, 2006. ,