Tensors versus matrices usefulness and unexpected properties
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[1] Lieven De Lathauwer,et al. A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization , 2006, SIAM J. Matrix Anal. Appl..
[2] Lieven De Lathauwer,et al. An enhanced line search scheme for complex-valued tensor decompositions. Application in DS-CDMA , 2008, Signal Process..
[3] Lieven De Lathauwer,et al. A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic I˟J˟2 Arrays , 2008, SIAM J. Matrix Anal. Appl..
[4] Pierre Comon,et al. Enhanced Line Search: A Novel Method to Accelerate PARAFAC , 2008, SIAM J. Matrix Anal. Appl..
[5] G. Bergman. Ranks of tensors and change of base field , 1969 .
[6] Pierre Comon,et al. Decomposition of quantics in sums of powers of linear forms , 1996, Signal Process..
[7] F. L. Hitchcock. Multiple Invariants and Generalized Rank of a P‐Way Matrix or Tensor , 1928 .
[8] Andrzej Cichocki,et al. Nonnegative Matrix and Tensor Factorization T , 2007 .
[9] P. Comon,et al. Blind separation of discrete sources , 1998, IEEE Signal Processing Letters.
[10] J. Kruskal. Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .
[11] A. Iarrobino,et al. Power Sums, Gorenstein Algebras, and Determinantal Loci , 2000 .
[12] P. Paatero. The Multilinear Engine—A Table-Driven, Least Squares Program for Solving Multilinear Problems, Including the n-Way Parallel Factor Analysis Model , 1999 .
[13] Pierre Comon,et al. Blind channel identification and extraction of more sources than sensors , 1998, Optics & Photonics.
[14] Michael Greenacre,et al. Multiway data analysis , 1992 .
[15] Phillip A. Regalia,et al. On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors , 2001, SIAM J. Matrix Anal. Appl..
[16] P. McCullagh. Tensor Methods in Statistics , 1987 .
[17] Joos Vandewalle,et al. On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..
[18] Rasmus Bro,et al. A comparison of algorithms for fitting the PARAFAC model , 2006, Comput. Stat. Data Anal..
[19] Gian-Carlo Rota,et al. Apolarity and Canonical Forms for Homogeneous Polynomials , 1993, Eur. J. Comb..
[20] D. Weinberg. Canonical forms for symmetric tensors , 1984 .
[21] Pierre Comon,et al. Blind identification of under-determined mixtures based on the characteristic function , 2006, Signal Process..
[22] Boris N. Khoromskij,et al. Hierarchical Kronecker tensor-product approximations , 2005, J. Num. Math..
[23] J. Chang,et al. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .
[24] Susan A. Murphy,et al. Monographs on statistics and applied probability , 1990 .
[25] Nikos D. Sidiropoulos,et al. Blind PARAFAC receivers for DS-CDMA systems , 2000, IEEE Trans. Signal Process..
[26] J. Berge,et al. The typical rank of tall three-way arrays , 2000 .
[27] Liqun Qi,et al. Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines , 2006, J. Symb. Comput..
[28] Lars Kai Hansen,et al. Parallel Factor Analysis as an exploratory tool for wavelet transformed event-related EEG , 2006, NeuroImage.
[29] Joos Vandewalle,et al. Computation of the Canonical Decomposition by Means of a Simultaneous Generalized Schur Decomposition , 2005, SIAM J. Matrix Anal. Appl..
[30] T. Howell,et al. Global properties of tensor rank , 1978 .
[31] Lek-Heng Lim,et al. Singular values and eigenvalues of tensors: a variational approach , 2005, 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2005..
[32] Pierre Comon,et al. Tensor Decompositions, State of the Art and Applications , 2002 .
[33] Pierre Comon,et al. Symmetric tensor decomposition , 2009, 2009 17th European Signal Processing Conference.
[34] V. Strassen. Rank and optimal computation of generic tensors , 1983 .
[35] L. Lathauwer,et al. On the Best Rank-1 and Rank-( , 2004 .
[36] P. Comon,et al. Tensor decompositions, alternating least squares and other tales , 2009 .
[37] Nikos D. Sidiropoulos,et al. Parallel factor analysis in sensor array processing , 2000, IEEE Trans. Signal Process..
[38] H. Sebastian Seung,et al. Learning the parts of objects by non-negative matrix factorization , 1999, Nature.
[39] Max Welling,et al. Positive tensor factorization , 2001, Pattern Recognit. Lett..
[40] Grazia Lotti,et al. Approximate Solutions for the Bilinear Form Computational Problem , 1980, SIAM J. Comput..
[41] P. Kroonenberg. Applied Multiway Data Analysis , 2008 .
[42] Mark D. Plumbley. Conditions for nonnegative independent component analysis , 2002, IEEE Signal Processing Letters.
[43] Vin de Silva,et al. Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.
[44] Marc Moreno Maza,et al. Computation of canonical forms for ternary cubics , 2002, ISSAC '02.
[45] Michael Clausen,et al. Typical Tensorial Rank , 1997 .
[46] Gene H. Golub,et al. Symmetric Tensors and Symmetric Tensor Rank , 2008, SIAM J. Matrix Anal. Appl..
[47] P. Paatero. Construction and analysis of degenerate PARAFAC models , 2000 .
[48] George Salmon. Lessons introductory to the modern higher algebra , 1885 .
[49] Anthony Iarrobino,et al. Inverse System of a Symbolic Power II. The Waring Problem for Forms , 1995 .
[50] Pierre Comon,et al. Subtracting a best rank-1 approximation may increase tensor rank , 2009, 2009 17th European Signal Processing Conference.
[51] Tamara G. Kolda,et al. Categories and Subject Descriptors: G.4 [Mathematics of Computing]: Mathematical Software— , 2022 .
[52] Pierre Comon,et al. Nonnegative approximations of nonnegative tensors , 2009, ArXiv.
[53] Pierre Comon,et al. Analytical blind discrete source separation , 2000, 2000 10th European Signal Processing Conference.
[54] Joe W. Harris,et al. Algebraic Geometry: A First Course , 1995 .
[55] N. Sidiropoulos,et al. On the uniqueness of multilinear decomposition of N‐way arrays , 2000 .
[56] Rasmus Bro,et al. Improving the speed of multiway algorithms: Part II: Compression , 1998 .
[57] P. Comon,et al. Higher-order power method - application in independent component analysis , 1995 .
[58] P. Comon,et al. Generic and typical ranks of multi-way arrays , 2009 .
[59] Pierre Comon,et al. Blind identification of under-determined mixtures based on the characteristic function , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..