CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping
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[1] F. L. Hitchcock. Multiple Invariants and Generalized Rank of a P‐Way Matrix or Tensor , 1928 .
[2] L. Tucker,et al. Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.
[3] J. Chang,et al. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .
[4] Richard A. Harshman,et al. Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .
[5] J. Kruskal. Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .
[6] B. Kowalski,et al. Tensorial resolution: A direct trilinear decomposition , 1990 .
[7] A. Franc. Etude algébrique des multitableaux : apports de l'algèbre tensorielle , 1992 .
[8] Andy Harter,et al. Parameterisation of a stochastic model for human face identification , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.
[9] Ben C. Mitchell,et al. Slowly converging parafac sequences: Swamps and two‐factor degeneracies , 1994 .
[10] B. Kowalski,et al. Error analysis of the generalized rank annihilation method , 1994 .
[11] J. Pernier,et al. Stimulus Specificity of Phase-Locked and Non-Phase-Locked 40 Hz Visual Responses in Human , 1996, The Journal of Neuroscience.
[12] R. Harshman,et al. Relating two proposed methods for speedup of algorithms for fitting two- and three-way principal component and related multilinear models , 1997 .
[13] P. Paatero. A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis , 1997 .
[14] P. Paatero,et al. THREE-WAY (PARAFAC) FACTOR ANALYSIS : EXAMINATION AND COMPARISON OF ALTERNATIVE COMPUTATIONAL METHODS AS APPLIED TO ILL-CONDITIONED DATA , 1998 .
[15] Henk A. L. Kiers,et al. A three–step algorithm for CANDECOMP/PARAFAC analysis of large data sets with multicollinearity , 1998 .
[16] Rasmus Bro,et al. Improving the speed of multi-way algorithms:: Part I. Tucker3 , 1998 .
[17] Rasmus Bro,et al. MULTI-WAY ANALYSIS IN THE FOOD INDUSTRY Models, Algorithms & Applications , 1998 .
[18] Nicholas D. Sidiropoulos,et al. Parafac techniques for signal separation , 2000 .
[19] Rasmus Bro,et al. The N-way Toolbox for MATLAB , 2000 .
[20] Joos Vandewalle,et al. A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..
[21] 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..
[22] N. Sidiropoulos,et al. On the uniqueness of multilinear decomposition of N‐way arrays , 2000 .
[23] P. Paatero. Construction and analysis of degenerate PARAFAC models , 2000 .
[24] Nikos D. Sidiropoulos,et al. Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays , 2001, IEEE Trans. Signal Process..
[25] Ilghiz Ibraghimov,et al. Application of the three‐way decomposition for matrix compression , 2002, Numer. Linear Algebra Appl..
[26] R. Bro,et al. Practical aspects of PARAFAC modeling of fluorescence excitation‐emission data , 2003 .
[27] Rasmus Bro,et al. Multi-way Analysis with Applications in the Chemical Sciences , 2004 .
[28] Amy Nicole Langville,et al. A Kronecker product approximate preconditioner for SANs , 2004, Numer. Linear Algebra Appl..
[29] L. Lathauwer,et al. On the Best Rank-1 and Rank-( , 2004 .
[30] William S Rayens,et al. Structure-seeking multilinear methods for the analysis of fMRI data , 2004, NeuroImage.
[31] Pierre Comon,et al. Enhanced Line Search: A Novel Method to Accelerate PARAFAC , 2008, SIAM J. Matrix Anal. Appl..
[32] Tamir Hazan,et al. Non-negative tensor factorization with applications to statistics and computer vision , 2005, ICML.
[33] Boris N. Khoromskij,et al. Hierarchical Kronecker tensor-product approximations , 2005, J. Num. Math..
[34] David E. Booth,et al. Multi-Way Analysis: Applications in the Chemical Sciences , 2005, Technometrics.
[35] Lieven De Lathauwer,et al. A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization , 2006, SIAM J. Matrix Anal. Appl..
[36] Lars Kai Hansen,et al. Parallel Factor Analysis as an exploratory tool for wavelet transformed event-related EEG , 2006, NeuroImage.
[37] Lieven De Lathauwer,et al. Tensor-based techniques for the blind separation of DS-CDMA signals , 2007, Signal Process..
[38] A. Stegeman,et al. On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition , 2007 .
[39] Lars Kai Hansen,et al. ERPWAVELAB A toolbox for multi-channel analysis of time–frequency transformed event related potentials , 2007, Journal of Neuroscience Methods.
[40] Boris N. Khoromskij,et al. Mathematik in den Naturwissenschaften Leipzig Tensor-Product Approximation to Operators and Functions in High Dimensions , 2007 .
[41] L. De Lathauwer,et al. Canonical decomposition of even higher order cumulant arrays for blind underdetermined mixture identification , 2008, 2008 5th IEEE Sensor Array and Multichannel Signal Processing Workshop.
[42] Vin de Silva,et al. Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.
[43] A. Stegeman,et al. On the Non-Existence of Optimal Solutions and the Occurrence of “Degeneracy” in the CANDECOMP/PARAFAC Model , 2008, Psychometrika.
[44] M. Haardt,et al. A closed-form solution for multilinear PARAFAC decompositions , 2008, 2008 5th IEEE Sensor Array and Multichannel Signal Processing Workshop.
[45] Michael W. Berry,et al. Discussion Tracking in Enron Email using PARAFAC. , 2008 .
[46] Lieven De Lathauwer,et al. Blind Identification of Underdetermined Mixtures by Simultaneous Matrix Diagonalization , 2008, IEEE Transactions on Signal Processing.
[47] P. Comon,et al. Tensor decompositions, alternating least squares and other tales , 2009 .
[48] Richard A. Harshman,et al. An efficient algorithm for Parafac with uncorrelated mode‐A components applied to large I × J × K data sets with I >> JK , 2009 .
[49] Pierre Comon,et al. Tensors versus matrices usefulness and unexpected properties , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.
[50] F. Chinesta,et al. Recent advances on the use of separated representations , 2009 .
[51] A. Stegeman. Using the simultaneous generalized Schur decomposition as a Candecomp/Parafac algorithm for ill‐conditioned data , 2009 .
[52] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[53] Eugene E. Tyrtyshnikov,et al. Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions , 2009, SIAM J. Sci. Comput..
[54] Andrzej Cichocki,et al. Nonnegative Matrix and Tensor Factorization T , 2007 .
[55] Zbynek Koldovský,et al. Simultaneous search for all modes in multilinear models , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.
[56] Alwin Stegeman,et al. On Uniqueness of the nth Order Tensor Decomposition into Rank-1 Terms with Linear Independence in One Mode , 2010, SIAM J. Matrix Anal. Appl..
[57] A. Cichocki,et al. Tensor decompositions for feature extraction and classification of high dimensional datasets , 2010 .
[58] P. Constantine,et al. A Surrogate Accelerated Bayesian Inverse Analysis of the HyShot II Supersonic Combustion Data , 2010 .
[59] P. Tichavský,et al. Stability analysis and fast damped-gauss-newton algorithm for INDSCAL tensor decomposition , 2011, 2011 IEEE Statistical Signal Processing Workshop (SSP).
[60] Pierre Comon,et al. Blind Identification of Underdetermined Mixtures Based on the Characteristic Function: The Complex Case , 2011, IEEE Transactions on Signal Processing.
[61] Andrzej Cichocki,et al. Fast damped gauss-newton algorithm for sparse and nonnegative tensor factorization , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
[62] Daniel M. Dunlavy,et al. A scalable optimization approach for fitting canonical tensor decompositions , 2011 .
[63] Jorge N. Tendeiro,et al. Some New Results on Orthogonally Constrained Candecomp , 2011, J. Classif..
[64] Tamara G. Kolda,et al. Temporal Link Prediction Using Matrix and Tensor Factorizations , 2010, TKDD.
[65] Pierre Comon,et al. Computing the polyadic decomposition of nonnegative third order tensors , 2011, Signal Process..
[66] Zbynek Koldovský,et al. Weight Adjusted Tensor Method for Blind Separation of Underdetermined Mixtures of Nonstationary Sources , 2011, IEEE Transactions on Signal Processing.
[67] Alwin Stegeman,et al. On Uniqueness of the Canonical Tensor Decomposition with Some Form of Symmetry , 2011, SIAM J. Matrix Anal. Appl..
[68] Liqun Qi,et al. New ALS Methods With Extrapolating Search Directions and Optimal Step Size for Complex-Valued Tensor Decompositions , 2011, IEEE Transactions on Signal Processing.
[69] Zbynek Koldovský,et al. Stability of CANDECOMP-PARAFAC tensor decomposition , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
[70] L. Lathauwer,et al. Canonical Polyadic Decomposition with Orthogonality Constraints , 2012 .
[71] Pierre Comon,et al. CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives , 2012, IEEE Transactions on Signal Processing.
[72] Eugene E. Tyrtyshnikov,et al. Fast truncation of mode ranks for bilinear tensor operations , 2012, Numer. Linear Algebra Appl..
[73] A. Atsawarungruangkit,et al. Generating Correlation Matrices Based on the Boundaries of Their Coefficients , 2012, PloS one.
[74] Alwin Stegeman,et al. Candecomp/Parafac: From Diverging Components to a Decomposition in Block Terms , 2012, SIAM J. Matrix Anal. Appl..
[75] Charles Van Loan,et al. Block Tensor Unfoldings , 2011, SIAM J. Matrix Anal. Appl..
[76] Andrzej Cichocki,et al. On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms , 2012, ArXiv.
[77] Laurent Albera,et al. Multi-way space-time-wave-vector analysis for EEG source separation , 2012, Signal Process..
[78] Pierre Comon,et al. Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix , 2012, SIAM J. Matrix Anal. Appl..
[79] Andrzej Cichocki,et al. Low Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC , 2012, SIAM J. Matrix Anal. Appl..
[80] Zbynek Koldovský,et al. Cramér-Rao-Induced Bounds for CANDECOMP/PARAFAC Tensor Decomposition , 2012, IEEE Transactions on Signal Processing.
[81] Andrzej Cichocki,et al. A further improvement of a fast damped Gauss-Newton algorithm for candecomp-parafac tensor decomposition , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.
[82] Andrzej Cichocki,et al. Fast Alternating LS Algorithms for High Order CANDECOMP/PARAFAC Tensor Factorizations , 2013, IEEE Transactions on Signal Processing.
[83] Pierre Comon,et al. Blind Multilinear Identification , 2012, IEEE Transactions on Information Theory.