Computation of low-rank tensor approximation under existence constraint via a forward-backward algorithm
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Pierre Comon | Khalid Minaoui | Marouane Nazih | Elaheh Sobhani | P. Comon | K. Minaoui | Elaheh Sobhani | Marouane Nazih
[1] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[2] Pierre Comon,et al. Coherence Constrained Alternating Least Squares , 2018, 2018 26th European Signal Processing Conference (EUSIPCO).
[3] Andrzej Cichocki,et al. Partitioned Alternating Least Squares Technique for Canonical Polyadic Tensor Decomposition , 2016, IEEE Signal Processing Letters.
[4] Mohamed-Jalal Fadili,et al. Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity, by Jean-Luc Starck, Fionn Murtagh, and Jalal M. Fadili , 2010, J. Electronic Imaging.
[5] A. Stegeman,et al. On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition , 2007 .
[6] Tamara G. Kolda,et al. Orthogonal Tensor Decompositions , 2000, SIAM J. Matrix Anal. Appl..
[7] L. Tucker,et al. Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.
[8] A. Geramita,et al. Ranks of tensors, secant varieties of Segre varieties and fat points , 2002 .
[9] Pierre Comon,et al. Tensor Decompositions, State of the Art and Applications , 2002 .
[10] Rasmus Bro,et al. Improving the speed of multi-way algorithms:: Part I. Tucker3 , 1998 .
[11] Marc Teboulle,et al. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..
[12] B. Kowalski,et al. Tensorial resolution: A direct trilinear decomposition , 1990 .
[13] Pinar Çivicioglu,et al. Backtracking Search Optimization Algorithm for numerical optimization problems , 2013, Appl. Math. Comput..
[14] Souleymen Sahnoun,et al. Joint Source Estimation and Localization , 2015, IEEE Transactions on Signal Processing.
[15] Andrzej Cichocki,et al. Partitioned Hierarchical alternating least squares algorithm for CP tensor decomposition , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
[16] Nikos D. Sidiropoulos,et al. Blind PARAFAC receivers for DS-CDMA systems , 2000, IEEE Trans. Signal Process..
[17] J. Kruskal,et al. How 3-MFA data can cause degenerate parafac solutions, among other relationships , 1989 .
[18] Yurii Nesterov,et al. Gradient methods for minimizing composite functions , 2012, Mathematical Programming.
[19] Huan Li,et al. Accelerated Proximal Gradient Methods for Nonconvex Programming , 2015, NIPS.
[20] J. Kruskal. Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .
[21] Pierre Comon,et al. Blind Multilinear Identification , 2012, IEEE Transactions on Information Theory.
[22] C. G. Bollini,et al. On the Reduction Formula of Feinberg and Pais , 1965 .
[23] M. Fukushima,et al. A generalized proximal point algorithm for certain non-convex minimization problems , 1981 .
[24] Richard A. Harshman,et al. Determination and Proof of Minimum Uniqueness Conditions for PARAFAC1 , 1972 .
[25] Michael Elad,et al. Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.
[26] Na Li,et al. Some Convergence Results on the Regularized Alternating Least-Squares Method for Tensor Decomposition , 2011, 1109.3831.
[27] Richard A. Harshman,et al. Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .
[28] E. Lee,et al. APPLYING GRADIENT PROJECTION AND CONJUGATE GRADIENT TO THE OPTIMUM OPERATION OF RESERVOIRS1 , 1970 .
[29] Pierre Comon,et al. Enhanced Line Search: A Novel Method to Accelerate PARAFAC , 2008, SIAM J. Matrix Anal. Appl..
[30] Stephen P. Boyd,et al. Proximal Algorithms , 2013, Found. Trends Optim..
[31] E. Candès,et al. Sparsity and incoherence in compressive sampling , 2006, math/0611957.
[32] Lieven De Lathauwer,et al. A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization , 2006, SIAM J. Matrix Anal. Appl..
[33] Khalid Minaoui,et al. A progression strategy of proximal algorithm for the unconstrained optimization , 2018, 2018 4th International Conference on Optimization and Applications (ICOA).
[34] R. Bro,et al. Fluorescence spectroscopy and multi-way techniques. PARAFAC , 2013 .
[35] Lieven De Lathauwer,et al. On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors - Part I: Basic Results and Uniqueness of One Factor Matrix , 2013, SIAM J. Matrix Anal. Appl..
[36] Pierre Comon,et al. Using the proximal gradient and the accelerated proximal gradient as a canonical polyadic tensor decomposition algorithms in difficult situations , 2020, Signal Process..
[37] Caroline Fossati,et al. Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis , 2012, IEEE Transactions on Geoscience and Remote Sensing.
[38] J. Chang,et al. Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .
[39] P. Paatero. Construction and analysis of degenerate PARAFAC models , 2000 .
[40] Benar Fux Svaiter,et al. Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods , 2013, Math. Program..
[41] Patrick L. Combettes,et al. Proximal Splitting Methods in Signal Processing , 2009, Fixed-Point Algorithms for Inverse Problems in Science and Engineering.
[42] F. L. Hitchcock. The Expression of a Tensor or a Polyadic as a Sum of Products , 1927 .
[43] Pierre Comon,et al. ROBUST INDEPENDENT COMPONENT ANALYSIS , 2009 .
[44] Pierre Comon,et al. Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size , 2010, IEEE Transactions on Neural Networks.
[45] P. Paatero. A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis , 1997 .
[46] Christian Jutten,et al. Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..
[47] Rasmus Bro,et al. Improving the speed of multiway algorithms: Part II: Compression , 1998 .
[48] Andrzej Cichocki,et al. Low Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC , 2012, SIAM J. Matrix Anal. Appl..
[49] H. Kiers. Towards a standardized notation and terminology in multiway analysis , 2000 .
[50] Vin de Silva,et al. Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.
[51] Jacek Gondzio,et al. Interior point methods 25 years later , 2012, Eur. J. Oper. Res..
[52] W. Rayens,et al. Two-factor degeneracies and a stabilization of PARAFAC , 1997 .
[53] Bijan Afsari,et al. Sensitivity Analysis for the Problem of Matrix Joint Diagonalization , 2008, SIAM J. Matrix Anal. Appl..
[54] Driss Aboutajdine,et al. CP decomposition approach to blind separation for DS-CDMA system using a new performance index , 2014, EURASIP J. Adv. Signal Process..
[55] Nico Vervliet,et al. Nonconvex Optimization Tools for Large-Scale Matrix and Tensor Decomposition with Structured Factors , 2020, ArXiv.
[56] Ben C. Mitchell,et al. Slowly converging parafac sequences: Swamps and two‐factor degeneracies , 1994 .
[57] Pierre Comon,et al. Tensors : A brief introduction , 2014, IEEE Signal Processing Magazine.
[58] Stephen P. Boyd,et al. Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.
[59] S. Leurgans,et al. A Decomposition for Three-Way Arrays , 1993, SIAM J. Matrix Anal. Appl..
[60] P. Comon,et al. Tensor decompositions, alternating least squares and other tales , 2009 .