-
1
-
-
0013019287
-
Differentiation of pseudo-inverses, separable nonlinear least square problems and other tales
-
Nashed MZ (ed.). Academic Press: New York
-
Golub GH, Pereyra V. Differentiation of pseudo-inverses, separable nonlinear least square problems and other tales. In Generalized Inverses and Applications, Nashed MZ (ed.). Academic Press: New York, 1976; 303-324.
-
(1976)
Generalized Inverses and Applications
, pp. 303-324
-
-
Golub, G.H.1
Pereyra, V.2
-
3
-
-
33750178584
-
Tensor-based techniques for the blind separation of DS-CDMA signals
-
DeLathauwer L, Castaing J. Tensor-based techniques for the blind separation of DS-CDMA signals. Signal Processing 2007; 87(2): 322-336.
-
(2007)
Signal Processing
, vol.87
, Issue.2
, pp. 322-336
-
-
deLathauwer, L.1
Castaing, J.2
-
4
-
-
33750148453
-
PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization
-
de Almeida ALF, Favier G, Mota JCM. PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization. Signal Processing 2007; 87(2): 337-351.
-
(2007)
Signal Processing
, vol.87
, Issue.2
, pp. 337-351
-
-
de Almeida, A.L.F.1
Favier, G.2
Mota, J.C.M.3
-
5
-
-
0346238834
-
Tensor decompositions
-
In, McWhirter JG, Proudler IK (eds). Clarendon Press: Oxford, UK
-
Comon P. Tensor decompositions. In Mathematics in Signal Processing V, McWhirter JG, Proudler IK (eds). Clarendon Press: Oxford, UK, 2002; 1-24.
-
(2002)
Mathematics in Signal Processing V
, pp. 1-24
-
-
Comon, P.1
-
6
-
-
48749101457
-
Three-way arrays: Rank and uniqueness of trilinear decompositions
-
Kruskal JB. Three-way arrays: Rank and uniqueness of trilinear decompositions. Linear Algebra Appl. 1977; 18: 95-138.
-
(1977)
Linear Algebra Appl.
, vol.18
, pp. 95-138
-
-
Kruskal, J.B.1
-
7
-
-
0039957423
-
Rank and optimal computation of generic tensors
-
Strassen V. Rank and optimal computation of generic tensors. Linear Algebra Appl. 1983; 52: 645-685.
-
(1983)
Linear Algebra Appl.
, vol.52
, pp. 645-685
-
-
Strassen, V.1
-
10
-
-
0030813663
-
Parafac, tutorial and applications
-
Bro R. Parafac, tutorial and applications. Chemom. Intel. Lab. Syst. 1997; 38: 149-171.
-
(1997)
Chemom. Intel. Lab. Syst.
, vol.38
, pp. 149-171
-
-
Bro, R.1
-
11
-
-
33745916802
-
Blind identification of under-determined mixtures based on the characteristic function
-
Comon P, Rajih M. Blind identification of under-determined mixtures based on the characteristic function. Signal Processing 2006; 86(9): 2271-2281.
-
(2006)
Signal Processing
, vol.86
, Issue.9
, pp. 2271-2281
-
-
Comon, P.1
Rajih, M.2
-
12
-
-
0003052447
-
How 3-MFA data can cause degenerate Parafac solutions, among other relationships
-
In, Coppi R, Bolasco S (eds). Elsevier Science: North-Holland
-
Kruskal JB, Harshman RA, Lundy ME. How 3-MFA data can cause degenerate Parafac solutions, among other relationships. In Multiway Data Analysis, Coppi R, Bolasco S (eds). Elsevier Science: North-Holland, 1989; 115-121.
-
(1989)
Multiway Data Analysis
, pp. 115-121
-
-
Kruskal, J.B.1
Harshman, R.A.2
Lundy, M.E.3
-
13
-
-
66849099206
-
Enhanced line search: A novel method to accelerate PARAFAC. SIAM
-
Rajih M, Comon P, Harshman R. Enhanced line search: a novel method to accelerate PARAFAC. SIAM J. Matrix Anal. Appl. 2008; 30(3): 1148-1171.
-
(2008)
J. Matrix Anal. Appl.
, vol.30
, Issue.3
, pp. 1148-1171
-
-
Rajih, M.1
Comon, P.2
Harshman, R.3
-
14
-
-
84984320741
-
Slowly converging Parafac sequences: Swamps and two-factor degeneracies
-
Mitchell BC, Burdick DS. Slowly converging Parafac sequences: Swamps and two-factor degeneracies. J. Chemom. 1994; 8: 155-168.
-
(1994)
J. Chemom.
, vol.8
, pp. 155-168
-
-
Mitchell, B.C.1
Burdick, D.S.2
-
15
-
-
0030730107
-
Two-factor degeneracies and a stabilization of Parafac
-
Rayens WS, Mitchell BC. Two-factor degeneracies and a stabilization of Parafac. Chemom. Intell. Lab. Syst. 1997; 38: 173-181.
-
(1997)
Chemom. Intell. Lab. Syst
, vol.38
, pp. 173-181
-
-
Rayens, W.S.1
Mitchell, B.C.2
-
16
-
-
0033653782
-
Construction and analysis of degenerate Parafac models. J
-
Paatero P. Construction and analysis of degenerate Parafac models. J. Chemom. 2000; 14: 285-299.
-
(2000)
Chemom
, vol.14
, pp. 285-299
-
-
Paatero, P.1
-
18
-
-
0000020580
-
Kruskal's polynomial for 2×2×2 arrays and a generalization to 2 × n × n arrays
-
ten Berge JMF. Kruskal's polynomial for 2×2×2 arrays and a generalization to 2 × n × n arrays. Psychometrika 1991; 56: 631-636.
-
(1991)
Psychometrika
, vol.56
, pp. 631-636
-
-
ten Berge, J.M.F.1
-
19
-
-
33751214191
-
Degeneracy in Candecomp/Parafac explained for p × p×2 arrays of rank p+1 or higher
-
Stegeman A. Degeneracy in Candecomp/Parafac explained for p × p×2 arrays of rank p+1 or higher. Psychometrika 2006;71(3):483-501.
-
(2006)
Psychometrika
, vol.71
, Issue.3
, pp. 483-501
-
-
Stegeman, A.1
-
20
-
-
38949176012
-
Degeneracy in Candecomp/Parafac and Indscal explained for several three-sliced arrays with a two-valued typical rank
-
Stegeman A. Degeneracy in Candecomp/Parafac and Indscal explained for several three-sliced arrays with a two-valued typical rank. Psychometrika 2007; 72(4): 601-619.
-
(2007)
Psychometrika
, vol.72
, Issue.4
, pp. 601-619
-
-
Stegeman, A.1
-
21
-
-
64749087756
-
Symmetric tensors and symmetric tensor rank
-
Comon P, Golub G, Lim L-H, Mourrain B. Symmetric tensors and symmetric tensor rank. SIAM J. Matrix Anal. Appl. 2008; 30(3): 1254-1279.
-
(2008)
SIAM J. Matrix Anal. Appl.
, vol.30
, Issue.3
, pp. 1254-1279
-
-
Comon, P.1
Golub, G.2
Lim, L.-H.3
Mourrain, B.4
-
22
-
-
55349142218
-
Tensor rank and the ill-posedness of the best low- rank approximation problem
-
De Silva V, Lim L-H. Tensor rank and the ill-posedness of the best low- rank approximation problem. SIAM J. Matrix Anal. Appl. 2008; 30(3): 1084-1127.
-
(2008)
SIAM J. Matrix Anal. Appl.
, vol.30
, Issue.3
, pp. 1084-1127
-
-
de Silva, V.1
Lim, L.-H.2
-
23
-
-
52949104087
-
On the non-existence of optimal solutions and the occurrence of degeneracy in the Candecomp/Parafac model
-
Krijnen WP, Dijkstra TK, Stegeman A. On the non-existence of optimal solutions and the occurrence of degeneracy in the Candecomp/Parafac model. Psychometrika 2008; 73(3): 431-439.
-
(2008)
Psychometrika
, vol.73
, Issue.3
, pp. 431-439
-
-
Krijnen, W.P.1
Dijkstra, T.K.2
Stegeman, A.3
-
24
-
-
52949146687
-
Low-rank approximation of generic p × q × 2 arrays and diverging components in the Candecomp/Parafac model
-
Stegeman A. Low-rank approximation of generic p × q × 2 arrays and diverging components in the Candecomp/Parafac model. SIAM J. Matrix Anal. Appl. 2008; 30(3): 988-1007.
-
(2008)
SIAM J. Matrix Anal. Appl.
, vol.30
, Issue.3
, pp. 988-1007
-
-
Stegeman, A.1
-
25
-
-
85013370154
-
Border rank of a p × q × 2 tensor and the optimal approximation of a pair of bilinear forms
-
Springer-Verlag: London, UK
-
Bini D. Border rank of a p × q × 2 tensor and the optimal approximation of a pair of bilinear forms. In Proceedings of the 7th Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 85. Springer-Verlag:London, UK, 1980; 98-108.
-
(1980)
Proceedings of the 7th Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science
, vol.85
, pp. 98-108
-
-
Bini, D.1
-
26
-
-
46149133798
-
Border rank of m × n × (mn - q) tensors
-
Bini D. Border rank of m × n × (mn - q) tensors. Linear Algebra Appl. 1986; 79: 45-51.
-
(1986)
Linear Algebra Appl.
, vol.79
, pp. 45-51
-
-
Bini, D.1
-
27
-
-
36049038610
-
An enhanced line search scheme for complex-valued tensor decompositions. application in DS-CDMA
-
Nion D, DeLathauwer L. An enhanced line search scheme for complex-valued tensor decompositions. application in DS-CDMA. Signal Processing 2008; 88(3): 749-755.
-
(2008)
Signal Processing
, vol.88
, Issue.3
, pp. 749-755
-
-
Nion, D.1
deLathauwer, L.2
-
29
-
-
0032563557
-
Improving the speed of multiway algorithms. part ii: Compression
-
Bro R, Andersson CA. Improving the speed of multiway algorithms. part ii: Compression. Chemom. Intell. Lab. Syst. 1998; 42(1-2): 105-113.
-
(1998)
Chemom. Intell. Lab. Syst.
, vol.42
, Issue.1-2
, pp. 105-113
-
-
Bro, R.1
Andersson, C.A.2
-
30
-
-
85163188929
-
Multiple invariants and generalized rank of a p-way matrix or tensor
-
Hitchcock FL. Multiple invariants and generalized rank of a p-way matrix or tensor. J. Math. Phys. 1927; 7(1): 39-79.
-
(1927)
J. Math. Phys
, vol.7
, Issue.1
, pp. 39-79
-
-
Hitchcock, F.L.1
-
31
-
-
34250499792
-
Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition
-
Carroll JD, Chang JJ. Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition. Psychometrika 1970; 35(3): 283-319.
-
(1970)
Psychometrika
, vol.35
, Issue.3
, pp. 283-319
-
-
Carroll, J.D.1
Chang, J.J.2
-
32
-
-
0002740437
-
Foundations of the Parafac procedure: Models and con- ditions for an explanatory multimodal factor analysis
-
Harshman RA. Foundations of the Parafac procedure: Models and con- ditions for an explanatory multimodal factor analysis. UCLA Working Papers in Phonetics 1970; 16: 1-84. http://publish.uwo.ca/harshman.
-
(1970)
UCLA Working Papers in Phonetics
, vol.16
, pp. 1-84
-
-
Harshman, R.A.1
-
33
-
-
85153556537
-
-
Parafac: Parallel factor analysis. Computational Statistics and Data Analysis
-
Harshman RA, Lundy ME. Parafac: Parallel factor analysis. Computational Statistics and Data Analysis 1994; 39-72.
-
(1994)
Lundy ME
, pp. 39-72
-
-
Harshman, R.A.1
-
36
-
-
34249835584
-
La methode d'Horace eclatee: Application a l'interpolation en degre quatre
-
Alexander J, Hirschowitz A. La methode d'Horace eclatee: application a l'interpolation en degre quatre. Invent. Math. 1992; 107(3): 585-602.
-
(1992)
Invent. Math.
, vol.107
, Issue.3
, pp. 585-602
-
-
Alexander, J.1
Hirschowitz, A.2
-
37
-
-
0003908675
-
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
-
Undergraduate Texts in Mathematics. Springer Verlag: New York, 1992; 2nd edition in
-
Cox D, Little J, O'Shea D. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. Springer Verlag: New York, 1992; 2nd edition in 1996.
-
(1996)
-
-
Cox, D.1
Little, J.2
O'Shea, D.3
-
38
-
-
0030234706
-
Decomposition of quantics in sums of powers of linear forms
-
Special Issue on High-Order Statistics
-
Comon P, Mourrain B. Decomposition of quantics in sums of powers of linear forms. Signal Processing, Elsevier 1996; 53(2): 93-107; Special Issue on High-Order Statistics.
-
(1996)
Signal Processing, Elsevier
, vol.53
, Issue.2
, pp. 93-107
-
-
Comon, P.1
Mourrain, B.2
-
39
-
-
0033095689
-
Canonical forms of two by two matrices
-
Ehrenborg R. Canonical forms of two by two matrices. Jour. of Algebra 1999; 213: 195-224.
-
(1999)
Jour. of Algebra
, vol.213
, pp. 195-224
-
-
Ehrenborg, R.1
-
40
-
-
0002093582
-
On the theory of linear transformation
-
Cayley A. On the theory of linear transformation. Cambridge Math. J. 1845; 4: 193-209.
-
(1845)
Cambridge Math. J
, vol.4
, pp. 193-209
-
-
Cayley, A.1
-
41
-
-
70349696077
-
Nonnegative approximations of nonnegative tensors
-
this issue
-
Lim L-H, Comon P. Nonnegative approximations of nonnegative tensors. J. Chemom., 2009, this issue.
-
(2009)
J. Chemom.
-
-
Lim, L.-H.1
Comon, P.2
-
42
-
-
80053414448
-
Swamp reducing technique for tensor decomposition
-
In 16th European Signal Processing Conference (Eusipco'08), Lausanne August
-
Navasca C, De Lathauwer L, Kindermann S. Swamp reducing technique for tensor decomposition. In 16th European Signal Processing Conference (Eusipco'08), Lausanne, 25-29 August 2008.
-
(2008)
, pp. 25-29
-
-
Navasca, C.1
de Lathauwer, L.2
Kindermann, S.3
-
43
-
-
70349717885
-
Sulla rappresentazione delle forme quaternarie mediante somme di potenze di forme lineari. Atti della R
-
Terracini A. Sulla rappresentazione delle forme quaternarie mediante somme di potenze di forme lineari. Atti della R. Acc. delle Scienze di Torino 1916; 51: 107-117.
-
(1916)
Acc. Delle Scienze di Torino
, vol.51
, pp. 107-117
-
-
Terracini, A.1
-
44
-
-
0000973495
-
Kanonische formen
-
Lasker E. Kanonische formen. Math. Annal. 1904; 58: 434-440.
-
(1904)
Math. Annal.
, vol.58
, pp. 434-440
-
-
Lasker, E.1
-
45
-
-
33845756412
-
Singularities of linear systems and the Waring problem
-
Mella M. Singularities of linear systems and the Waring problem. Trans. Am. Math. Soc. 2006; 358(12): 5523-5538.
-
(2006)
Trans. Am. Math. Soc.
, vol.358
, Issue.12
, pp. 5523-5538
-
-
Mella, M.1
-
46
-
-
85153546233
-
Generic and typical ranks of three-way arrays
-
In Icassp'08, Las Vegas, 30 March-4 April
-
Comon P, ten Berge J. Generic and typical ranks of three-way arrays. In Icassp'08, Las Vegas, 30 March-4 April 2008.
-
(2008)
-
-
Comon, P.1
ten Berge, J.2
-
48
-
-
0007725617
-
Typical tensorial rank
-
Lickteig T. Typical tensorial rank. Linear Algebra Appl. 1985; 69: 95-120.
-
(1985)
Linear Algebra Appl
, vol.69
, pp. 95-120
-
-
Lickteig, T.1
-
49
-
-
43749106074
-
Induction for secant varieties of Segre varieties
-
August, arXiv:math/0607191
-
Abo H, Ottaviani G, Peterson C. Induction for secant varieties of Segre varieties, August 2006. arXiv:math/0607191.
-
(2006)
-
-
Abo, H.1
Ottaviani, G.2
Peterson, C.3
-
50
-
-
2642580865
-
Partial uniqueness in CANDECOMP/PARAFAC. Jour
-
ten Berge JMF. Partial uniqueness in CANDECOMP/PARAFAC. Jour. Chemometrics 2004; 18: 12-16.
-
(2004)
Chemometrics
, vol.18
, pp. 12-16
-
-
ten Berge, J.M.F.1
-
51
-
-
0034559666
-
The typical rank of tall three-way arrays
-
ten Berge JMF. The typical rank of tall three-way arrays. Psychometrika 2000; 65(5): 525-532.
-
(2000)
Psychometrika
, vol.65
, Issue.5
, pp. 525-532
-
-
ten Berge, J.M.F.1
-
52
-
-
33747839474
-
Symmetry transformations for square sliced three way arrays, with applications to their typical rank
-
ten Berge JMF, Stegeman A. Symmetry transformations for square sliced three way arrays, with applications to their typical rank. Linear Algebra Appl. 2006; 418: 215-224.
-
(2006)
Linear Algebra Appl.
, vol.418
, pp. 215-224
-
-
ten Berge, J.M.F.1
Stegeman, A.2
-
53
-
-
0041595584
-
Simplicity of core arrays in three-way principal component analysis and the typical rank of p × q × 2 arrays
-
ten Berge JMF, Kiers HAL. Simplicity of core arrays in three-way principal component analysis and the typical rank of p × q × 2 arrays. Linear Algebra Appl. 1999; 294: 169-179.
-
(1999)
Linear Algebra Appl.
, vol.294
, pp. 169-179
-
-
ten Berge, J.M.F.1
Kiers, H.A.L.2
-
54
-
-
33646373945
-
On the concept of k-sectant order of a variety
-
Chiantini L, Ciliberto C. On the concept of k-sectant order of a variety. J. London Math. Soc. 2006; 73(2): 436-454.
-
(2006)
J. London Math. Soc.
, vol.73
, Issue.2
, pp. 436-454
-
-
Chiantini, L.1
Ciliberto, C.2
-
55
-
-
33750991900
-
On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
-
Stegeman A, Sidiropoulos ND. On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition. Linear Algebra Appl. 2007; 420: 540-552.
-
(2007)
Linear Algebra Appl.
, vol.420
, pp. 540-552
-
-
Stegeman, A.1
Sidiropoulos, N.D.2
-
56
-
-
70349721177
-
Kruskal's Theorem
-
private communication
-
Landsberg JM. Kruskal's Theorem, 2008, private communication.
-
(2008)
-
-
Landsberg, J.M.1
-
57
-
-
0033653594
-
On the uniqueness of multilinear decomposition of N-way arrays
-
Sidiropoulos ND, Bro R. On the uniqueness of multilinear decomposition of N-way arrays. J. Chemom. 2000; 14: 229-239.
-
(2000)
J. Chemom.
, vol.14
, pp. 229-239
-
-
Sidiropoulos, N.D.1
Bro, R.2
-
58
-
-
33746356349
-
A link between canonical decomposition in multilinear algebra and simultaneous matrix diagonalization
-
DeLathauwer L. A link between canonical decomposition in multilinear algebra and simultaneous matrix diagonalization. SIAM J. Matrix Anal. 2006; 28(3): 642-666.
-
(2006)
SIAM J. Matrix Anal.
, vol.28
, Issue.3
, pp. 642-666
-
-
DeLathauwer, L.1
-
59
-
-
0004087635
-
-
volume 15 of Series in Computer Science. World Scientific Publication: London
-
Rissanen J. Stochastic Complexity in Statistical Inquiry, volume 15 of Series in Computer Science. World Scientific Publication: London, 1989.
-
(1989)
Stochastic Complexity in Statistical Inquiry
-
-
Rissanen, J.1
-
60
-
-
0034144761
-
On the best rank-1 and rank- (R1,R2,... RN) approximation of high-order tensors
-
DeLathauwer L, de Moor B, Vandewalle J. On the best rank-1 and rank- (R1,R2,... RN) approximation of high-order tensors. SIAM J. Matrix Anal. Appl. 2000; 21(4): 1324-1342.
-
(2000)
SIAM J. Matrix Anal. Appl.
, vol.21
, Issue.4
, pp. 1324-1342
-
-
deLathauwer, L.1
de Moor, B.2
Vandewalle, J.3
-
61
-
-
0003436776
-
Linear Statistical Inference and its Applications
-
Wiley: New York
-
Rao CR. Linear Statistical Inference and its Applications. Probability and Statistics. Wiley: New York, 1965.
-
(1965)
Probability and Statistics
-
-
Rao, C.R.1
-
63
-
-
0013953617
-
Some mathematical notes for three-mode factor analysis
-
Tucker LR. Some mathematical notes for three-mode factor analysis. Psychometrika 1966; 31: 279-311.
-
(1966)
Psychometrika
, vol.31
, pp. 279-311
-
-
Tucker, L.R.1
-
64
-
-
0033275630
-
The multilinear engine: A table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model
-
Paatero P. The multilinear engine: A table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model. J. Comput. Graph. Stat. 1999; 8(4): 854-888.
-
(1999)
J. Comput. Graph. Stat.
, vol.8
, Issue.4
, pp. 854-888
-
-
Paatero, P.1
-
65
-
-
30144444694
-
A comparison of algorithms for fitting the Parafac model
-
Tomasi G, Bro R. A comparison of algorithms for fitting the Parafac model. Comp. Stat. Data Anal. 2006; 50: 1700-1734.
-
(2006)
Comp. Stat. Data Anal.
, vol.50
, pp. 1700-1734
-
-
Tomasi, G.1
Bro, R.2
-
67
-
-
70350521208
-
Enhanced line search: A novel method to accelerate Parafac
-
In Eusipco'05, Antalya, Turkey, September
-
Rajih M, Comon P. Enhanced line search: A novel method to accelerate Parafac. In Eusipco'05, Antalya, Turkey, 4-8 September 2005.
-
(2005)
, pp. 4-8
-
-
Rajih, M.1
Comon, P.2
-
69
-
-
84946063031
-
An improved algorithm for computing the singular value decomposition. ACM Trans. Math
-
Chan TF. An improved algorithm for computing the singular value decomposition. ACM Trans. Math. Soft. 1982; 8(1): 72-83.
-
(1982)
Soft
, vol.8
, Issue.1
, pp. 72-83
-
-
Chan, T.F.1
-
70
-
-
0025474239
-
Tracking of a few extreme singular values and vectors in signal processing
-
(published from Stanford report 78NA-89-01, February 1989)
-
Comon P, Golub GH. Tracking of a few extreme singular values and vectors in signal processing. Proceedings of the IEEE 1990; 78(8): 1327-1343 (published from Stanford report 78NA-89-01, February 1989).
-
(1990)
Proceedings of the IEEE
, vol.78
, Issue.8
, pp. 1327-1343
-
-
Comon, P.1
Golub, G.H.2
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