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Tensors: a Brief Introduction (2014)
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by Pierre Comon
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10 - 3 self
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Citations
721
Tensor decompositions and applications
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Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart–Young” decomposition, Psychometrika 35 (3
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Foundations of the PARAFAC procedure: models and conditions for an exploratory multi-mode factor analysis
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466
A multilinear singular value decomposition
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424
Some mathematical notes on three-mode factor analysis
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310
Three-way arrays: Rank and uniqueness of trilinear decompositions
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194
Tensor rank and the ill-posedness of the best low-rank approximation problem
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155
Handbook of Blind Source Separation: Independent Component Analysis and Applications
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143
Polynomial interpolation in several variables.
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125
Giannakis, “Parallel factor analysis in sensor array processing
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123
Orthogonal tensor decompositions
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118
Singular values and eigenvalues of tensors: a variational approach
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113
Multi-way Analysis
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106
On the Best Rank-1 And Rank-(R1,R2, ... ,RN) Approximation Of Higher-Order Tensors
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106
L.: The expression of a tensor or a polyadic as a sum of products
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100
On the uniqueness of multilinear decomposition of N-way arrays
- Sidiropoulos, Bro - 2000
99
Symmetric tensors and symmetric tensor rank
- Comon, Golub, et al. - 2008
86
Towards a standardized notation and terminology in multiway analysis
- Kiers - 2000
81
A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization
- DeLathauwer
79
Tensors: Geometry and Applications
- Landsberg - 2012
79
Joint approximate diagonalization of positive definite hermitian matrices
- Pham - 2001
76
Sums of even powers of reallinear forms
- Reznick
76
and optimal computations of generic tensors
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73
A comparison of algorithms for fitting the PARAFAC model,
- Tomasi, Bro - 2006
57
Enhanced line search: a novel method to accelerate
- Rajih, Comon, et al. - 2008
55
Induction for secant varieties of Segre varieties
- Abo, Ottaviani, et al.
55
Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition.
- Lathauwer, Moor, et al. - 2004
50
de Almeida, Tensor decompositions, alternating least squares and other tales
- Comon, Luciani, et al.
50
Partial and total matrix multiplication
- Schönhage - 1981
48
Apolarity and canonical forms for homogeneous polynomials
- Ehrenborg, Rota - 1993
48
Kruskal’s permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models.
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47
Tensor decompositions: state of the art and applications. InMathematics in signal processing,
- Comon - 2000
45
Most tensor problems are NP-hard
- Hillar, Lim
45
A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation
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44
Computing symmetric rank for symmetric tensors,
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39
A decomposition for three-way arrays,
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39
Comon, Nonnegative approximations of nonnegative tensors
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38
On Kruskal’s uniqueness condition for the CANDECOMP/PARAFAC decomposition
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33
Linear Systems of Plane Curves
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32
Construction and analysis of degenerate PARAFAC models
- Paatero
29
Symmetric tensor decomposition,
- Brachat, Comon, et al. - 2010
29
Tensor methods
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28
Improving the speed of multi-way algorithms
- Andersson, Bro - 1998
28
Generic and typical ranks of multi-way arrays.
- Berge, Castaing, et al. - 2009
25
X.D.: Nonorthogonal joint diagonalization free of degenerate solution
- Li, Zhang - 2007
23
Independent component analysis and (simultaneous) third-order tensor diagonalization
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20
Global properties of tensor rank
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20
Lathauwer, “Optimizationbased algorithms for tensor decompositions: Canonical Polyadic Decomposition, decomposition in rank-(Lr , Lr , 1) terms and a new generalization
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19
Inverse system of a symbolic power. II. The Waring problem for forms.
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17
K.: Quadratic optimization for simultaneous matrix diagonalization
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16
Weight Adjusted Tensor Method for Blind Separation of Underdetermined Mixtures of Nonstationary Sources,
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15
On generic identifiability of 3-tensors of small rank
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15
Eigenvectors of tensors and algorithms for Waring decomposition
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15
Lathauwer, A method to avoid diverging components in the Candecomp/Parafac model for generic
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14
Tensor Approximation and Signal Processing Applications
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13
A concise proof of Kruskal’s theorem on tensor decomposition. Linear Algebra and its Applications
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11
separation of exponential polynomials and the decomposition of a tensor in rank-(Lr
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11
Canonical polyadic decomposition of third-order tensors: Reduction to generalized eigenvalue decomposition
- Domanov, Lathauwer - 2014
10
a tool for blind source separation using fourth order statistics only
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10
rank one approximation of real symmetric tensors can be chosen symmetric, Front
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10
The number of singular vector tuples and uniqueness of best rank one approximation of tensors
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9
usefulness and unexpected properties
- Comon, “Tensors
9
Semi-algebraic canonical decomposition of multi-way arrays and joint eigenvalue decomposition
- Luciani, Albera - 2011
8
Kruskal’s polynomial for 2×2×2 arrays and a generalization 2× n× n arrays, Psychometrika 56
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8
On the best rank-1 approximation to higher-order symmetric tensors
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8
Non-orthogonal joint diagoinalization in the LS sense with application in blind source separation
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8
The best rank-1 approximation of a symmetric tensor and related spherical optimization problems
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7
From vectors to tensors, Universitext
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6
Generic and typical ranks of three-way arrays
- COMON, BERGE
6
On the typical rank of real binary forms.
- Comon, Ottaviani - 2009
6
multilinear identification
- Lim, Comon, et al.
6
Computing the polyadic decomposition of nonnegative third order tensors
- Royer, T-Moreau, et al. - 2011
6
Subtracting a best rank-1 approximation does not necessarily decrease tensor rank
- Stegeman, Comon
4
On the maximum rank of a real binary form. Annali di Matematica Pura ed Applicata
- Causa, Re - 2011
4
On the best rank-1 approximation of higher-order symmetric tensors
- Kofidis, Ph
4
Tensor decompositions with banded matrix factors, Linear Algebra and its Applications
- Sorensen, Comon - 2013
3
O(n2.77) complexity for nxn approximate matrix multiplication
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3
Typical real ranks of binary forms
- Blekherman
3
A.: Joint matrices decompositions and blind source separation: A survey of methods, identification, and applications
- Chabriel, Kleinsteuber, et al. - 2014
3
Laws of inertia in higher degree binary forms
- Reznick - 2010
3
M.: A semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalizations
- Röemer, Haardt - 2013
2
Numerical performance of a tensor MUSIC algorithm based on HOSVD for a mixture of polarized sources
- Boizard, Ginolhac, et al. - 2013
2
Ranks of N-way arrays and the Geometry of 2x2x2 arrays
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2
Tensor completion through multiple Kronecker product decomposition
- Phan, Cichocki, et al.
1
Mandic et al., “Multi-way component analysis for tensor data: a signal processing perspective
- Cichocki, D - 2013
1
Tensor decompositions, a geometric viewpoint”, 2014, being submitted
- Comon, Ottaviani
1
Candecomp/Parafac decomposition of high-order tensors through tensor reshaping
- Phan, Tichavsky, et al. - 2013
1
Three-Mode Company. http://three-mode.leidenuniv.nl ha l-0 9, v er sio n - 3 Ju l 2
- Kroonenberg