-
1
-
-
0005332910
-
Ranks of tensors and change of base field
-
G. M. BERGMAN, "Ranks of tensors and change of base field," Journal of Algebra, vol. 11, pp. 613-621, 1969.
-
(1969)
Journal of Algebra
, vol.11
, pp. 613-621
-
-
BERGMAN, G.M.1
-
3
-
-
0007725617
-
Typical tensorial rank
-
T. LICKTEIG, "Typical tensorial rank," Linear Algebra Appl., vol. 69, pp. 95-120, 1985.
-
(1985)
Linear Algebra Appl
, vol.69
, pp. 95-120
-
-
LICKTEIG, T.1
-
4
-
-
64749087756
-
Symmetric tensors and symmetric tensor rank
-
P. COMON, G. GOLUB, L-H. LIM, and B. MOURRAIN, "Symmetric tensors and symmetric tensor rank," SIAM Jour. Matrix Ana. Appl., vol. 30, no. 3, pp. 1254-1279, 2008.
-
(2008)
SIAM Jour. Matrix Ana. Appl
, vol.30
, Issue.3
, pp. 1254-1279
-
-
COMON, P.1
GOLUB, G.2
LIM, L.-H.3
MOURRAIN, B.4
-
5
-
-
35348895048
-
Multiple invariants and generalized rank of a p-way matrix or tensor
-
F. L. HITCHCOCK, "Multiple invariants and generalized rank of a p-way matrix or tensor," J. Math. and Phys., vol. 7, no. 1, pp. 40-79, 1927.
-
(1927)
J. Math. and Phys
, vol.7
, Issue.1
, pp. 40-79
-
-
HITCHCOCK, F.L.1
-
6
-
-
0007772789
-
Global properties of tensor rank
-
T. D. HOWELL, "Global properties of tensor rank," Linear Algebra and Applications, vol. 22, pp. 9-23, 1978.
-
(1978)
Linear Algebra and Applications
, vol.22
, pp. 9-23
-
-
HOWELL, T.D.1
-
7
-
-
48749142095
-
Canonical forms for symmetric tensors
-
D. A. WEINSTEIN, "Canonical forms for symmetric tensors," Linear Algebra Appl., pp. 271-282, 1984.
-
(1984)
Linear Algebra Appl
, pp. 271-282
-
-
WEINSTEIN, D.A.1
-
8
-
-
72349100096
-
Symmetric tensor decomposition
-
submitted. hal:inria-00355713, arXiv:0901.3706
-
J. BRACHAT, P. COMON, B. MOURRAIN, and E. TSI-GARIDAS, "Symmetric tensor decomposition," Linear Algebra and its Applications, 2009, submitted. hal:inria-00355713, arXiv:0901.3706.
-
(2009)
Linear Algebra and its Applications
-
-
BRACHAT, J.1
COMON, P.2
MOURRAIN, B.3
TSI-GARIDAS, E.4
-
9
-
-
72349092379
-
-
P. COMON, Tensor decompositions, state of the art and applications, in Mathematics in Signal Processing V, J. G. McWhirter and I. K. Proudler, Eds., pp. 1-24. Clarendon Press, Oxford, UK, 2002, arXiv:0905.0454v1.
-
P. COMON, "Tensor decompositions, state of the art and applications," in Mathematics in Signal Processing V, J. G. McWhirter and I. K. Proudler, Eds., pp. 1-24. Clarendon Press, Oxford, UK, 2002, arXiv:0905.0454v1.
-
-
-
-
10
-
-
33846606151
-
Singular values and eigenvalues of tensors: A variational approach
-
Puerto Vallarta, Mexico, 13-15 Dec
-
L-H. LIM, "Singular values and eigenvalues of tensors: a variational approach," in IEEE Int. Workshop on Comput. Adv. Multi-Sensor Adapt. Proc., Puerto Vallarta, Mexico, 13-15 Dec. 2005.
-
(2005)
IEEE Int. Workshop on Comput. Adv. Multi-Sensor Adapt. Proc
-
-
LIM, L.-H.1
-
11
-
-
0032224093
-
Blind channel identification and extraction of more sources than sensors, keynote address
-
San Diego, July 19-24
-
P. COMON, "Blind channel identification and extraction of more sources than sensors," keynote address. in SPIE Conference, San Diego, July 19-24 1998, pp. 2-13,
-
(1998)
SPIE Conference
, pp. 2-13
-
-
COMON, P.1
-
12
-
-
33750796673
-
Rank and eigenvalues of a symmetric tensor, the multivariate homogeneous polynomial and the algebraic hyper-surface it defines
-
L. QI, "Rank and eigenvalues of a symmetric tensor, the multivariate homogeneous polynomial and the algebraic hyper-surface it defines," Jour.Symbolic Computation, vol. 41, pp. 1309-1327, 2006.
-
(2006)
Jour.Symbolic Computation
, vol.41
, pp. 1309-1327
-
-
QI, L.1
-
13
-
-
0001536630
-
Apolarity and canonical forms for homogeneous polynomials
-
R. EHRENBORG and G. C. ROTA, "Apolarity and canonical forms for homogeneous polynomials," European Jour. Combinatorics, vol. 14, pp. 157-181, 1993.
-
(1993)
European Jour. Combinatorics
, vol.14
, pp. 157-181
-
-
EHRENBORG, R.1
ROTA, G.C.2
-
14
-
-
0001419778
-
Inverse system of a symbolic power. II. the Waring problem for forms
-
A. IARROBINO, "Inverse system of a symbolic power. II. the Waring problem for forms," J. Algebra, vol. 174, pp. 1091-1110, 1995.
-
(1995)
J. Algebra
, vol.174
, pp. 1091-1110
-
-
IARROBINO, A.1
-
15
-
-
0034559666
-
The typical rank of tall three-way arrays
-
Sept
-
J. M. F. ten BERGE, "The typical rank of tall three-way arrays," Psychometrika, vol. 65, no. 5, pp. 525-532, Sept. 2000.
-
(2000)
Psychometrika
, vol.65
, Issue.5
, pp. 525-532
-
-
ten BERGE, J.M.F.1
-
16
-
-
64749092635
-
Generic and typical ranks of multi-way arrays
-
June
-
P. COMON, J. M. F. ten BERGE, L. De LATHAUWER, and J. CASTAING, "Generic and typical ranks of multi-way arrays," Linear Algebra Appl., vol. 430, no. 11-12, pp. 2997-3007, June 2009.
-
(2009)
Linear Algebra Appl
, vol.430
, Issue.11-12
, pp. 2997-3007
-
-
COMON, P.1
ten BERGE, J.M.F.2
De LATHAUWER, L.3
CASTAING, J.4
-
17
-
-
0030234706
-
Decomposition of quantics in sums of powers of linear forms
-
special issue on High-Order Statistics, Sept
-
P. COMON and B. MOURRAIN, "Decomposition of quantics in sums of powers of linear forms," Signal Processing, Elsevier, vol. 53, no. 2, pp. 93-107, Sept. 1996, special issue on High-Order Statistics.
-
(1996)
Signal Processing, Elsevier
, vol.53
, Issue.2
, pp. 93-107
-
-
COMON, P.1
MOURRAIN, B.2
-
18
-
-
70349656252
-
Tensor decompositions, alternating least squares and other tales
-
P. COMON, X. LUCIANI, and A. L. F. de ALMEIDA, "Tensor decompositions, alternating least squares and other tales," Jour. Chemometrics, 2009.
-
(2009)
Jour. Chemometrics
-
-
COMON, P.1
LUCIANI, X.2
de ALMEIDA, A.L.F.3
-
19
-
-
0033653594
-
On the uniqueness of multilinear decomposition of N-way arrays
-
N. D. SIDIROPOULOS and R. BRO, "On the uniqueness of multilinear decomposition of N-way arrays," Jour. Chemo., vol. 14, pp. 229-239, 2000.
-
(2000)
Jour. Chemo
, vol.14
, pp. 229-239
-
-
SIDIROPOULOS, N.D.1
BRO, R.2
-
20
-
-
48749101457
-
Three-way arrays: Rank and uniqueness of trilinear decompositions
-
J. B. KRUSKAL, "Three-way arrays: Rank and uniqueness of trilinear decompositions," Linear Algebra and Applications, vol. 18, pp. 95-138, 1977.
-
(1977)
Linear Algebra and Applications
, vol.18
, pp. 95-138
-
-
KRUSKAL, J.B.1
-
21
-
-
33746356349
-
A link between canonical decomposition in multilinear algebra and simultaneous matrix diagonalization
-
L. De LATHAUWER, "A link between canonical decomposition in multilinear algebra and simultaneous matrix diagonalization," SIAM Jour. Matrix Ana. Appl., vol. 28, no. 3, pp. 642-666, 2006.
-
(2006)
SIAM Jour. Matrix Ana. Appl
, vol.28
, Issue.3
, pp. 642-666
-
-
De LATHAUWER, L.1
-
23
-
-
0036042351
-
Computation of canonical forms for ternary cubics
-
ACM
-
I. A. KOGAN and M. M. MAZA, "Computation of canonical forms for ternary cubics," in ISSAC. 2000, pp. 151-160, ACM.
-
(2000)
ISSAC
, pp. 151-160
-
-
KOGAN, I.A.1
MAZA, M.M.2
-
24
-
-
72349090575
-
Subtracting a best rank-1 approximation does not necessarily decrease tensor rank
-
Glasgow, Scotland, Aug. 24-28
-
A. STEGEMAN and P. COMON, "Subtracting a best rank-1 approximation does not necessarily decrease tensor rank," in EUSIPCO'09, Glasgow, Scotland, Aug. 24-28 2009.
-
(2009)
EUSIPCO'09
-
-
STEGEMAN, A.1
COMON, P.2
-
25
-
-
55349142218
-
Tensor rank and the ill-posedness of the best low-rank approximation problem
-
V. De SILVA and L-H. LIM, "Tensor rank and the ill-posedness of the best low-rank approximation problem," SIAM Jour. Matrix Ana. Appl., vol. 30, no. 3, pp. 1084-1127, 2008.
-
(2008)
SIAM Jour. Matrix Ana. Appl
, vol.30
, Issue.3
, pp. 1084-1127
-
-
De SILVA, V.1
LIM, L.-H.2
-
26
-
-
0000144406
-
Algebraic Geometry, a first course
-
of, Springer
-
J. HARRIS, Algebraic Geometry, a first course, vol. 133 of Graduate Texts in Math., Springer, 1992.
-
(1992)
Graduate Texts in Math
, vol.133
-
-
HARRIS, J.1
-
27
-
-
2142824430
-
Analytical blind discrete source separation
-
Tampere, Finland, 5-8 sept
-
O. GRELLIER and P. COMON, "Analytical blind discrete source separation," in Eusipco, Tampere, Finland, 5-8 sept. 2000.
-
(2000)
Eusipco
-
-
GRELLIER, O.1
COMON, P.2
-
28
-
-
0002883410
-
Higher-order power method, application in Independent Component Analysis
-
Las Vegas, 10-14 Dec
-
L. de LATHAUWER, P. COMON, et al., "Higher-order power method, application in Independent Component Analysis," in NOLTA Conference, Las Vegas, 10-14 Dec 1995, vol. 1, pp. 91-96.
-
(1995)
NOLTA Conference
, vol.1
, pp. 91-96
-
-
de LATHAUWER, L.1
COMON, P.2
-
29
-
-
0036018642
-
One the best rank-1 approximation of higher-order supersymmetric tensors
-
E. KOFIDIS and P. REGALIA, "One the best rank-1 approximation of higher-order supersymmetric tensors," SIAM Jour. Matrix Ana. Appl., vol. 23, pp. 863-884, 2002.
-
(2002)
SIAM Jour. Matrix Ana. Appl
, vol.23
, pp. 863-884
-
-
KOFIDIS, E.1
REGALIA, P.2
-
30
-
-
0034144761
-
On the best rank-1 and rank-(R1,R2,⋯RN) approximation of high-order tensors
-
Apr
-
L. de LATHAUWER, B. de MOOR, and J. VANDEWALLE, "On the best rank-1 and rank-(R1,R2,⋯RN) approximation of high-order tensors," SIAM Jour. Matrix Ana. Appl., vol. 21, no. 4, pp. 1324-1342, Apr. 2000.
-
(2000)
SIAM Jour. Matrix Ana. Appl
, vol.21
, Issue.4
, pp. 1324-1342
-
-
de LATHAUWER, L.1
de MOOR, B.2
VANDEWALLE, J.3
-
31
-
-
70349696077
-
Nonnegative approximations of nonnegative tensors
-
to appear
-
L-H. LIM and P. COMON, "Nonnegative approximations of nonnegative tensors," Jour. Chemometrics, 2009, to appear.
-
(2009)
Jour. Chemometrics
-
-
LIM, L.-H.1
COMON, P.2
-
32
-
-
0033653782
-
Construction and analysis of degenerate Parafac models
-
P. PAATERO, "Construction and analysis of degenerate Parafac models," Jour. Chemometrics, vol. 14, pp. 285-299, 2000.
-
(2000)
Jour. Chemometrics
, vol.14
, pp. 285-299
-
-
PAATERO, P.1
-
33
-
-
33645813863
-
Approximate solutions for the bilinear form computational problem
-
D. BINI, G. LOTTI, and F. ROMANI, "Approximate solutions for the bilinear form computational problem," SIAM Jour. Comput., pp. 692-697, 1980.
-
(1980)
SIAM Jour. Comput
, pp. 692-697
-
-
BINI, D.1
LOTTI, G.2
ROMANI, F.3
-
34
-
-
0033275630
-
The multilinear engine: A table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model
-
Dec
-
P. PAATERO, "The multilinear engine: A table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model," Journal of Computational and Graphical Statistics, vol. 8, no. 4, pp. 854-888, Dec. 1999.
-
(1999)
Journal of Computational and Graphical Statistics
, vol.8
, Issue.4
, pp. 854-888
-
-
PAATERO, P.1
-
35
-
-
30144444694
-
A comparison of algorithms for fitting the Parafac model
-
G. TOMASI and R. BRO, "A comparison of algorithms for fitting the Parafac model," Comp. Stat. Data Anal., vol. 50, pp. 1700-1734, 2006.
-
(2006)
Comp. Stat. Data Anal
, vol.50
, pp. 1700-1734
-
-
TOMASI, G.1
BRO, R.2
-
36
-
-
0032563557
-
Improving the speed of multiway algorithms. Part II: Compression
-
R. BRO and C. A. ANDERSSON, "Improving the speed of multiway algorithms. Part II: Compression," Chemometrics and Intelligent Laboratory Systems, vol. 42, no. 1-2, pp. 105-113, 1998.
-
(1998)
Chemometrics and Intelligent Laboratory Systems
, vol.42
, Issue.1-2
, pp. 105-113
-
-
BRO, R.1
ANDERSSON, C.A.2
-
39
-
-
66849099206
-
Enhanced line search: A novel method to accelerate Parafac
-
Sept
-
M. RAJIH, P. COMON, and R. HARSHMAN, "Enhanced line search: A novel method to accelerate Parafac," SIAM Jour. Matrix Ana. Appl., vol. 30, no. 3, pp. 1148-1171, Sept. 2008.
-
(2008)
SIAM Jour. Matrix Ana. Appl
, vol.30
, Issue.3
, pp. 1148-1171
-
-
RAJIH, M.1
COMON, P.2
HARSHMAN, R.3
-
40
-
-
36049038610
-
An enhanced line search scheme for complex-valued tensor decompositions. application in ds-cdma
-
Mar
-
D. NION and L. DeLATHAUWER, "An enhanced line search scheme for complex-valued tensor decompositions. application in ds-cdma," Signal Processing, vol. 88, no. 3, pp. 749-755, Mar. 2008.
-
(2008)
Signal Processing
, vol.88
, Issue.3
, pp. 749-755
-
-
NION, D.1
DeLATHAUWER, L.2
-
41
-
-
68649114427
-
A method to avoid diverging components in the Candecomp/Parafac model for generic IxJx2 arrays
-
A. STEGEMAN and L. De LATHAUWER, "A method to avoid diverging components in the Candecomp/Parafac model for generic IxJx2 arrays," SIAM J. Matrix Ana. Appl., vol. 30, pp. 1614-1638, 2009.
-
(2009)
SIAM J. Matrix Ana. Appl
, vol.30
, pp. 1614-1638
-
-
STEGEMAN, A.1
De LATHAUWER, L.2
-
42
-
-
17444379662
-
Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition
-
L. De LATHAUWER,B. De MOOR, and J. VANDEWALLE, "Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition," SIAM Jour. Matrix Ana. Appl., vol. 26, no. 2, pp. 295-327, 2004.
-
(2004)
SIAM Jour. Matrix Ana. Appl
, vol.26
, Issue.2
, pp. 295-327
-
-
De LATHAUWER, L.1
De MOOR, B.2
VANDEWALLE, J.3
-
43
-
-
21244436795
-
Hierarchical Kronecker tensor-product approximation
-
W. HACKBUSCH, B. N. KHOROMSKIJ, and E. E. TYRTYSHNIKOV, "Hierarchical Kronecker tensor-product approximation," Jour. Numer. Math., vol. 13, pp. 119-156, 2005.
-
(2005)
Jour. Numer. Math
, vol.13
, pp. 119-156
-
-
HACKBUSCH, W.1
KHOROMSKIJ, B.N.2
TYRTYSHNIKOV, E.E.3
-
44
-
-
0039957423
-
Rank and optimal computation of generic tensors
-
July
-
V. STRASSEN, "Rank and optimal computation of generic tensors," Linear Algebra Appl., vol. 52, pp. 645-685, July 1983.
-
(1983)
Linear Algebra Appl
, vol.52
, pp. 645-685
-
-
STRASSEN, V.1
-
45
-
-
0039324528
-
-
Springer
-
P.BÜRGISSER,M.CLAUSEN, and M. A. SHOKROLLAHI, Algebraic Complexity Theory, vol. 315, Springer, 1997.
-
(1997)
Algebraic Complexity Theory
, vol.315
-
-
BÜRGISSER, P.1
CLAUSEN, M.2
SHOKROLLAHI, M.A.3
-
47
-
-
33845525246
-
Algorithm 862: Matlab tensor classes for fast algorithm prototyping
-
B. W. BADER and T. KOLDA, "Algorithm 862: Matlab tensor classes for fast algorithm prototyping," ACM Trans. Math. Soft., vol. 32, pp. 635-653, 2006.
-
(2006)
ACM Trans. Math. Soft
, vol.32
, pp. 635-653
-
-
BADER, B.W.1
KOLDA, T.2
-
48
-
-
31044456392
-
-
M. MORUP and L. K. HANSEN et alterae, Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG, NeuroImage, 29, pp. 938-947, 2006.
-
M. MORUP and L. K. HANSEN et alterae, "Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG," NeuroImage, vol. 29, pp. 938-947, 2006.
-
-
-
-
49
-
-
34250499792
-
Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition
-
Sept
-
J. D. CARROLL and J. J. CHANG, "Analysis of individual differences in multidimensional scaling via n-way generalization of Eckart-Young decomposition," Psychometrika, vol. 35, no. 3, pp. 283-319, Sept. 1970.
-
(1970)
Psychometrika
, vol.35
, Issue.3
, pp. 283-319
-
-
CARROLL, J.D.1
CHANG, J.J.2
-
50
-
-
85032751966
-
Nonnegative matrix and tensor factorization
-
A. CICHOCKI, R. ZDUNEK, and S-I. AMARI, "Nonnegative matrix and tensor factorization," IEEE Sig. Proc. Mag., pp. 142-145, 2008.
-
(2008)
IEEE Sig. Proc. Mag
, pp. 142-145
-
-
CICHOCKI, A.1
ZDUNEK, R.2
AMARI, S.-I.3
-
51
-
-
0034861343
-
Positive tensor factorization
-
M. WELLING and M. WEBER, "Positive tensor factorization," Pattern Recognition Letters, vol. 22, no. 12, pp. 1255-1261, 2001.
-
(2001)
Pattern Recognition Letters
, vol.22
, Issue.12
, pp. 1255-1261
-
-
WELLING, M.1
WEBER, M.2
-
52
-
-
0036612776
-
Conditions for nonnegative independent component analysis
-
June
-
M. PLUMBLEY, "Conditions for nonnegative independent component analysis," Sig. Proc. Letters, vol. 9, pp. 177-180, June 2002.
-
(2002)
Sig. Proc. Letters
, vol.9
, pp. 177-180
-
-
PLUMBLEY, M.1
-
53
-
-
0033592606
-
Learning the parts of objects by non-negative matrix factorization
-
Oct
-
D. D. LEE and H. S. SEUNG, "Learning the parts of objects by non-negative matrix factorization.," Nature, vol. 401, pp. 788-791, Oct. 1999.
-
(1999)
Nature
, vol.401
, pp. 788-791
-
-
LEE, D.D.1
SEUNG, H.S.2
-
54
-
-
0034250083
-
Parallel factor analysis in sensor array processing
-
Aug
-
N. D. SIDIROPOULOS, R. BRO, and G. B. GIANNAKIS, "Parallel factor analysis in sensor array processing," IEEE Trans. Sig. Proc., vol. 48, no. 8, pp. 2377-2388, Aug. 2000.
-
(2000)
IEEE Trans. Sig. Proc
, vol.48
, Issue.8
, pp. 2377-2388
-
-
SIDIROPOULOS, N.D.1
BRO, R.2
GIANNAKIS, G.B.3
-
55
-
-
0033901839
-
Blind PARAFAC receivers for DS-CDMA systems
-
Mar
-
N. D. SIDIROPOULOS, G. B. GIANNAKIS, and R. BRO, "Blind PARAFAC receivers for DS-CDMA systems," IEEE Trans. on Sig. Proc., vol. 48, no. 3, pp. 810-823, Mar. 2000.
-
(2000)
IEEE Trans. on Sig. Proc
, vol.48
, Issue.3
, pp. 810-823
-
-
SIDIROPOULOS, N.D.1
GIANNAKIS, G.B.2
BRO, R.3
-
56
-
-
33745916802
-
Blind identification of under-determined mixtures based on the characteristic function
-
Sept
-
P. COMON and M. RAJIH, "Blind identification of under-determined mixtures based on the characteristic function," Signal Processing, vol. 86, no. 9, pp. 2271-2281, Sept. 2006.
-
(2006)
Signal Processing
, vol.86
, Issue.9
, pp. 2271-2281
-
-
COMON, P.1
RAJIH, M.2
|