Induction for secant varieties of Segre varieties, Transactions of the American Mathematical Society, vol.361, issue.02, pp.767-792, 2009. ,
DOI : 10.1090/S0002-9947-08-04725-9
ICAR: a tool for blind source separation using fourth-order statistics only, IEEE Transactions on Signal Processing, vol.53, issue.10, pp.3633-3643, 2005. ,
DOI : 10.1109/TSP.2005.855089
URL : https://hal.archives-ouvertes.fr/hal-00743890
Polynomial interpolation in several variables, J. Alg. Geom, vol.4, issue.2, pp.201-222, 1995. ,
Kruskal's polynomial for 2??2??2 arrays and a generalization to 2??n??n arrays, Psychometrika, vol.18, issue.4, pp.631-636, 1991. ,
DOI : 10.1007/BF02294495
Simplicity and typical rank of three-way arrays, with applications to Tucker-3 analysis with simple cores, Journal of Chemometrics, vol.18, issue.1, pp.17-21, 2004. ,
DOI : 10.1002/cem.840
Computing symmetric rank for symmetric tensors, Journal of Symbolic Computation, vol.46, issue.1, pp.34-53, 2011. ,
DOI : 10.1016/j.jsc.2010.08.001
URL : https://hal.archives-ouvertes.fr/hal-00645973
O(n2.7799) complexity for n ?? n approximate matrix multiplication, Information Processing Letters, vol.8, issue.5, pp.234-235, 1979. ,
DOI : 10.1016/0020-0190(79)90113-3
URL : https://hal.archives-ouvertes.fr/hal-00305432
Typical Real Ranks of Binary Forms, Foundations of Computational Mathematics, vol.138, issue.12, 2013. ,
DOI : 10.1007/s10208-013-9174-8
Numerical performance of a tensor MUSIC algorithm based on HOSVD, EUSIPCO, pp.13-15, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00871220
Symmetric tensor decomposition, Linear Algebra and its Applications, vol.433, issue.11-12, pp.1851-1872, 2010. ,
DOI : 10.1016/j.laa.2010.06.046
URL : https://hal.archives-ouvertes.fr/inria-00355713
Improving the speed of multiway algorithms. Part II: Compression, pp.105-113, 1998. ,
Analysis of individual differences in multidimensional scaling via an n-way generalization of ???Eckart-Young??? decomposition, Psychometrika, vol.12, issue.3, pp.283-319, 1970. ,
DOI : 10.1007/BF02310791
On the maximum rank of a real binary form, Annali di Matematica Pura ed Applicata, vol.212, issue.2, pp.55-59, 2011. ,
DOI : 10.1007/s10231-010-0137-2
Joint matrices decompositions and blind source separation, IEEE Sig. Proc. Magazine, vol.31, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01479802
On Generic Identifiability of 3-Tensors of Small Rank, Proc. Magazine, pp.1018-1037, 2012. ,
DOI : 10.1137/110829180
Tensor decompositions, state of the art and applications, Mathematics in Signal Processing, pp.1-24, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00347139
Tensors, usefulness and unexpected properties, 15th IEEE Workshop on Statistical Signal Processing, pp.781-788, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00417258
Symmetric Tensors and Symmetric Tensor Rank, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.3, pp.1254-1279, 2008. ,
DOI : 10.1137/060661569
URL : https://hal.archives-ouvertes.fr/hal-00327599
Tensor decompositions, alternating least squares and other tales, Journal of Chemometrics, vol.78, issue.8, pp.393-405, 2009. ,
DOI : 10.1016/j.laa.2009.01.014/
URL : https://hal.archives-ouvertes.fr/hal-00410057
On the typical rank of real binary forms, Linear and Multilinear Algebra, pp.657-667, 2012. ,
DOI : 10.1007/BF02296342
URL : https://hal.archives-ouvertes.fr/hal-00700790
Tensor decompositions, a geometric viewpoint, 2014. ,
Generic and typical ranks of multi-way arrays, Linear Algebra and its Applications, vol.430, issue.11-12, pp.11-12, 2009. ,
DOI : 10.1016/j.laa.2009.01.014
URL : https://hal.archives-ouvertes.fr/hal-00410058
A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization, SIAM Journal on Matrix Analysis and Applications, vol.28, issue.3, pp.642-666, 2006. ,
DOI : 10.1137/040608830
Blind separation of exponential polynomials and the decomposition of a tensor in rank-(Lr,Lr,1) terms, SIAM J. Matrix Anal. Appl, vol.32, issue.4, pp.145-1474, 2011. ,
A Multilinear Singular Value Decomposition, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1253-1278, 2000. ,
DOI : 10.1137/S0895479896305696
) Approximation of Higher-Order Tensors, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1324-1342, 2000. ,
DOI : 10.1137/S0895479898346995
Independent component analysis and (simultaneous) third-order tensor diagonalization, IEEE Transactions on Signal Processing, vol.49, issue.10, pp.2262-2271, 2001. ,
DOI : 10.1109/78.950782
Computation of the Canonical Decomposition by Means of a Simultaneous Generalized Schur Decomposition, SIAM Journal on Matrix Analysis and Applications, vol.26, issue.2, pp.295-327, 2004. ,
DOI : 10.1137/S089547980139786X
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. ,
DOI : 10.1137/120877234
On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part II: Uniqueness of the Overall Decomposition, SIAM Journal on Matrix Analysis and Applications, vol.34, issue.3, pp.876-903, 2013. ,
DOI : 10.1137/120877258
Apolarity and Canonical Forms for Homogeneous Polynomials, European Journal of Combinatorics, vol.14, issue.3, pp.157-181, 1993. ,
DOI : 10.1006/eujc.1993.1022
Best rank one approximation of real symmetric tensors can be chosen symmetric, Frontiers of Mathematics in China, vol.37, issue.1, pp.19-40, 2013. ,
DOI : 10.1007/s11464-012-0262-x
The Number of Singular Vector Tuples and Uniqueness of Best Rank-One Approximation of Tensors, Foundations of Computational Mathematics, vol.33, issue.2, 2012. ,
DOI : 10.1007/s10208-014-9194-z
Foundations of the Parafac procedure: Models and conditions for an explanatory multimodal factor analysis, UCLA Working Papers in Phonetics, vol.16, pp.1-84, 1970. ,
Most Tensor Problems Are NP-Hard, Journal of the ACM, vol.60, issue.6, 2012. ,
DOI : 10.1145/2512329
The Expression of a Tensor or a Polyadic as a Sum of Products, Journal of Mathematics and Physics, vol.6, issue.1-4, pp.165-189, 1927. ,
DOI : 10.1002/sapm192761164
Global properties of tensor rank, Linear Algebra and its Applications, vol.22, pp.9-23, 1978. ,
DOI : 10.1016/0024-3795(78)90052-6
Inverse System of a Symbolic Power II. The Waring Problem for Forms, Journal of Algebra, vol.174, issue.3, pp.1091-1110, 1995. ,
DOI : 10.1006/jabr.1995.1169
Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints, IEEE Transactions on Signal Processing, vol.52, issue.9, pp.2625-2636, 2004. ,
DOI : 10.1109/TSP.2004.832022
Towards a standardized notation and terminology in multiway analysis, Journal of Chemometrics, vol.56, issue.3, pp.105-122, 2000. ,
DOI : 10.1002/1099-128X(200005/06)14:3<105::AID-CEM582>3.0.CO;2-I
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.3, pp.863-884, 2002. ,
DOI : 10.1137/S0895479801387413
Tensor approximation and signal processing applications, Structured Matrices in Mathematics, 2001. ,
DOI : 10.1090/conm/280/04625
Orthogonal Tensor Decompositions, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.1, pp.243-255, 2001. ,
DOI : 10.1137/S0895479800368354
Tensor Decompositions and Applications, SIAM Review, vol.51, issue.3, pp.455-500, 2009. ,
DOI : 10.1137/07070111X
A Decomposition for Three-Way Arrays, SIAM Journal on Matrix Analysis and Applications, vol.14, issue.4, pp.1064-1083, 1993. ,
DOI : 10.1137/0614071
Nonorthogonal Joint Diagonalization Free of Degenerate Solution, IEEE Transactions on Signal Processing, vol.55, issue.5, pp.1803-1814, 2007. ,
DOI : 10.1109/TSP.2006.889983
Typical tensorial rank, Linear Algebra and its Applications, vol.69, pp.95-120, 1985. ,
DOI : 10.1016/0024-3795(85)90070-9
URL : http://doi.org/10.1016/0024-3795(85)90070-9
Singular values and eigenvalues of tensors: a variational approach, IEEE Int. Workshop on Comput. Adv. Multi-Sensor Adapt. Proc, pp.129-132, 2005. ,
Nonnegative approximations of nonnegative tensors, Journal of Chemometrics, vol.36, issue.3, pp.432-441, 2009. ,
DOI : 10.1002/cem.1244
URL : https://hal.archives-ouvertes.fr/hal-00410056
Blind Multilinear Identification, IEEE Transactions on Information Theory, vol.60, issue.2, pp.1260-1280, 2014. ,
DOI : 10.1109/TIT.2013.2291876
URL : https://hal.archives-ouvertes.fr/hal-00763275
Semi-algebraic canonical decomposition of multi-way arrays and Joint Eigenvalue Decomposition, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.4104-4107, 2011. ,
DOI : 10.1109/ICASSP.2011.5947255
URL : https://hal.archives-ouvertes.fr/hal-00595092
Tensor Methods in Statistics, Monographs on Statistics and Applied Probability, 1987. ,
Linear systems of plane curves, Notices of the AMS, vol.46, issue.2, pp.192-202, 1999. ,
On the best rank-1 approximation to higher-order symmetric tensors, Mathematical and Computer Modelling, vol.46, issue.9-10, pp.1345-1352, 2007. ,
DOI : 10.1016/j.mcm.2007.01.008
Eigenvectors of tensors and algorithms for Waring decomposition, Journal of Symbolic Computation, vol.54, pp.9-35, 2013. ,
DOI : 10.1016/j.jsc.2012.11.005
Construction and analysis of degenerate PARAFAC models, Journal of Chemometrics, vol.8, issue.3, pp.285-299, 2000. ,
DOI : 10.1002/1099-128X(200005/06)14:3<285::AID-CEM584>3.0.CO;2-1
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices, SIAM Journal on Matrix Analysis and Applications, vol.22, issue.4, pp.1136-1152, 2001. ,
DOI : 10.1137/S089547980035689X
Tensor completion through multiple Kronecker product decomposition, ICASSP'2013, pp.3233-3237, 2013. ,
CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping, IEEE Transactions on Signal Processing, vol.61, issue.19, pp.4847-4860, 2013. ,
DOI : 10.1109/TSP.2013.2269046
Enhanced Line Search: A Novel Method to Accelerate PARAFAC, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.3, pp.1148-1171, 2008. ,
DOI : 10.1137/06065577
URL : https://hal.archives-ouvertes.fr/hal-00327595
Sums of even powers of real linear forms, Memoirs of the American Mathematical Society, vol.96, issue.463, pp.1-155, 1992. ,
DOI : 10.1090/memo/0463
Laws of inertia in higher degree binary forms, Proceedings of the American Mathematical Society, vol.138, issue.03, pp.815-826, 2010. ,
DOI : 10.1090/S0002-9939-09-10186-7
A concise proof of Kruskal???s theorem on tensor decomposition, Linear Algebra and its Applications, vol.432, issue.7, pp.1818-1824, 2010. ,
DOI : 10.1016/j.laa.2009.11.033
A semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalizations (SECSI), Signal Processing, vol.93, issue.9, pp.2722-2738, 2013. ,
DOI : 10.1016/j.sigpro.2013.02.016
Computing the polyadic decomposition of nonnegative third order tensors, Signal Processing, vol.91, issue.9, pp.2159-2171, 2011. ,
DOI : 10.1016/j.sigpro.2011.03.006
URL : https://hal.archives-ouvertes.fr/hal-00618729
From Vectors to Tensors, 2005. ,
Partial and Total Matrix Multiplication, SIAM Journal on Computing, vol.10, issue.3, pp.434-455, 1981. ,
DOI : 10.1137/0210032
On the uniqueness of multilinear decomposition of N-way arrays, Journal of Chemometrics, vol.14, issue.3, pp.229-239, 2000. ,
DOI : 10.1002/1099-128X(200005/06)14:3<229::AID-CEM587>3.3.CO;2-E
Parallel factor analysis in sensor array processing, IEEE Transactions on Signal Processing, vol.48, issue.8, pp.2377-2388, 2000. ,
DOI : 10.1109/78.852018
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.3, pp.1084-1127, 2008. ,
DOI : 10.1137/06066518X
Multi-Way Analysis, 2004. ,
Optimization-Based Algorithms for Tensor Decompositions: Canonical Polyadic Decomposition, Decomposition in Rank-$(L_r,L_r,1)$ Terms, and a New Generalization, SIAM Journal on Optimization, vol.23, issue.2, pp.695-720, 2013. ,
DOI : 10.1137/120868323
Tensor decompositions with banded matrix factors, Linear Algebra and its Applications, vol.438, issue.2, pp.919-941, 2013. ,
DOI : 10.1016/j.laa.2011.10.044
URL : https://hal.archives-ouvertes.fr/hal-00740572
A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic $I\timesJ\times2$ Arrays, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.4, pp.1614-1638, 2009. ,
DOI : 10.1137/070692121
Subtracting a best rank-1 approximation may increase tensor rank, Linear Algebra and its Applications, vol.433, issue.7, pp.1276-1300, 2010. ,
DOI : 10.1016/j.laa.2010.06.027
URL : https://hal.archives-ouvertes.fr/hal-00435877
On Kruskal???s uniqueness condition for the Candecomp/Parafac decomposition, Linear Algebra and its Applications, vol.420, issue.2-3, pp.540-552, 2007. ,
DOI : 10.1016/j.laa.2006.08.010
Rank and optimal computation of generic tensors, Lin. Alg. Appl, vol.52, pp.645-685, 1983. ,
Weight Adjusted Tensor Method for Blind Separation of Underdetermined Mixtures of Nonstationary Sources, IEEE Transactions on Signal Processing, vol.59, issue.3, pp.1037-1047, 2011. ,
DOI : 10.1109/TSP.2010.2096221
A comparison of algorithms for fitting the PARAFAC model, Computational Statistics & Data Analysis, vol.50, issue.7, pp.1700-1734, 2006. ,
DOI : 10.1016/j.csda.2004.11.013
Some mathematical notes on three-mode factor analysis, Psychometrika, vol.64, issue.3, pp.279-311, 1966. ,
DOI : 10.1007/BF02289464
Quadratic optimization for simultaneous matrix diagonalization, IEEE Transactions on Signal Processing, vol.54, issue.9, pp.3270-3278, 2006. ,
DOI : 10.1109/TSP.2006.877673
Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation, IEEE Transactions on Signal Processing, vol.50, issue.7, pp.1545-1553, 2002. ,
DOI : 10.1109/TSP.2002.1011195
The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems, SIAM Journal on Matrix Analysis and Applications, vol.33, issue.3, pp.806-821, 2012. ,
DOI : 10.1137/110835335
A fast algorithm for joint diagonalization with non orthogonal transformations and its application to blind source separation, J. Machine Learning Research, vol.5, pp.777-800, 2004. ,