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Volumn 34, Issue 3, 2013, Pages 876-903

On the uniqueness of the canonical polyadic decomposition of third-order tensors-part II: Basic results and uniqueness of one factor matrix

Author keywords

Candecomp; Canonical polyadic decomposition; Compound matrix; Khatri Rao product; Multilinear algebra; Parafac; Tensor; Three way array

Indexed keywords

MATRIX ALGEBRA;

EID: 84886517932     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/120877258     Document Type: Article
Times cited : (141)

References (21)
  • 1
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an N-way generalization of "Eckart-Young" Decomposition
    • J. Carroll and J.-J. Chang, Analysis of individual differences in multidimensional scaling via an N-way generalization of "Eckart-Young" decomposition, Psychometrika, 35 (1970), pp. 283-319.
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carroll, J.1    Chang, J.-J.2
  • 2
    • 84867325862 scopus 로고    scopus 로고
    • On generic identifiability of 3-tensors of small rank
    • L. Chiantini and G. Ottaviani, On generic identifiability of 3-tensors of small rank, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 1018-1037.
    • (2012) SIAM J. Matrix Anal. Appl. , vol.33 , pp. 1018-1037
    • Chiantini, L.1    Ottaviani, G.2
  • 3
    • 70349656252 scopus 로고    scopus 로고
    • 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, J. Chemometrics, 23 (2009), pp. 393-405.
    • (2009) J. Chemometrics , vol.23 , pp. 393-405
    • Comon, P.1    Luciani, X.2    De Almeida, A.L.F.3
  • 4
    • 33746356349 scopus 로고    scopus 로고
    • A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization
    • L. De Lathauwer, A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 642-666.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 642-666
    • De Lathauwer, L.1
  • 5
    • 84856253450 scopus 로고    scopus 로고
    • Blind separation of exponential polynomials and the decomposition of a tensor in rank-(Lr, Lr, 1) terms
    • L. De Lathauwer, Blind separation of exponential polynomials and the decomposition of a tensor in rank-(Lr, Lr, 1) terms, SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1451-1474.
    • (2011) SIAM J. Matrix Anal. Appl. , vol.32 , pp. 1451-1474
    • De Lathauwer, L.1
  • 7
    • 84886455215 scopus 로고    scopus 로고
    • On the uniqueness of the canonical polyadic decomposition of third-order tensors-Part I: Basic results and uniqueness of one factor matrix
    • I. Domanov and L. De Lathauwer, On the uniqueness of the canonical polyadic decomposition of third-order tensors-Part I: Basic results and uniqueness of one factor matrix, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 855-875.
    • (2013) SIAM J. Matrix Anal. Appl. , vol.34 , pp. 855-875
    • Domanov, I.1    De Lathauwer, L.2
  • 8
    • 84861622498 scopus 로고    scopus 로고
    • Uni-mode and partial uniqueness conditions for CANDECOMP/PARAFAC of three-way arrays with linearly dependent loadings
    • X. Guo, S. Miron, D. Brie, and A. Stegeman, Uni-mode and partial uniqueness conditions for CANDECOMP/PARAFAC of three-way arrays with linearly dependent loadings, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 111-129.
    • (2012) SIAM J. Matrix Anal. Appl. , vol.33 , pp. 111-129
    • Guo, X.1    Miron, S.2    Brie, D.3    Stegeman, A.4
  • 10
    • 0035446680 scopus 로고    scopus 로고
    • Almost-sure identifiability of multidimensional harmonic retrieval
    • T. Jiang, N. D. Sidiropoulos, and J. M. F. Ten Berge, Almost-sure identifiability of multidimensional harmonic retrieval, IEEE Trans. Signal Process., 49 (2001), pp. 1849-1859.
    • (2001) IEEE Trans. Signal Process. , vol.49 , pp. 1849-1859
    • Jiang, T.1    Sidiropoulos, N.D.2    Ten Berge, J.M.F.3
  • 11
    • 4344616103 scopus 로고    scopus 로고
    • Kruskal's permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints
    • T. Jiang and N. D. Sidiropoulos, Kruskal's permutation lemma and the identification of CANDECOMP/PARAFAC and bilinear models with constant modulus constraints, IEEE Trans. Signal Process., 52 (2004), pp. 2625-2636.
    • (2004) IEEE Trans. Signal Process. , vol.52 , pp. 2625-2636
    • Jiang, T.1    Sidiropoulos, N.D.2
  • 12
    • 68649096448 scopus 로고    scopus 로고
    • Tensor decompositions and applications
    • T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Rev., 51 (2009), pp. 455-500.
    • (2009) SIAM Rev. , vol.51 , pp. 455-500
    • Kolda, T.G.1    Bader Bader, B.W.2
  • 14
    • 48749101457 scopus 로고
    • Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
    • J. B. Kruskal, Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear Algebra Appl., 18 (1977), pp. 95-138.
    • (1977) Linear Algebra Appl. , vol.18 , pp. 95-138
    • Kruskal, J.B.1
  • 15
    • 24644469120 scopus 로고    scopus 로고
    • Kruskal's condition for uniqueness in Candecomp/ Parafac when ranks and k-ranks coincide
    • A. Stegeman and J. M. F. Ten Berge, Kruskal's condition for uniqueness in Candecomp/ Parafac when ranks and k-ranks coincide, Comput. Statist. Data Anal., 50 (2006), pp. 210-220.
    • (2006) Comput. Statist. Data Anal. , vol.50 , pp. 210-220
    • Stegeman, A.1    Ten Berge, J.M.F.2
  • 16
    • 33746359652 scopus 로고    scopus 로고
    • Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
    • A. Stegeman, J. Ten Berge, and L. De Lathauwer, Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices, Psychometrika, 71 (2006), pp. 219-229.
    • (2006) Psychometrika , vol.71 , pp. 219-229
    • Stegeman, A.1    Ten Berge, J.2    De Lathauwer, L.3
  • 17
    • 65049083795 scopus 로고    scopus 로고
    • On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode
    • A. Stegeman, On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode, Linear Algebra Appl., 431 (2009), pp. 211-227.
    • (2009) Linear Algebra Appl. , vol.431 , pp. 211-227
    • Stegeman, A.1
  • 18
    • 0039957423 scopus 로고
    • Rank and optimal computation of generic tensors
    • V. Strassen, Rank and optimal computation of generic tensors, Linear Algebra Appl., 52-53 (1983), pp. 645-685.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 645-685
    • Strassen, V.1
  • 19
    • 3142774353 scopus 로고    scopus 로고
    • Typical rank and indscal dimensionality for symmetric three-way arrays of order i or i × 3 × 3, 2 × 2 or i × 3 × 3
    • J. M. F. Ten Berge, N. D. Sidiropoulos, and R. Rocci, Typical rank and indscal dimensionality for symmetric three-way arrays of order I × 2 × 2 or I × 3 × 3, Linear Algebra Appl., 388 (2004), pp. 363-377.
    • (2004) Linear Algebra Appl. , vol.388 , pp. 363-377
    • Ten Berge, J.M.F.1    Sidiropoulos, N.D.2    Rocci, R.3
  • 20
    • 2642580865 scopus 로고    scopus 로고
    • Partial uniqueness in CANDECOMP/PARAFAC
    • J. M. F. Ten Berge, Partial uniqueness in CANDECOMP/PARAFAC, J. Chemometrics, 18 (2004), pp. 12-16.
    • (2004) J. Chemometrics , vol.18 , pp. 12-16
    • Ten Berge, J.M.F.1
  • 21
    • 0035447407 scopus 로고    scopus 로고
    • Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays
    • L. Xiangqian and N. D. Sidiropoulos, Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays, IEEE Trans. Signal Process., 49 (2001), pp. 2074-2086.
    • (2001) IEEE Trans. Signal Process. , vol.49 , pp. 2074-2086
    • Xiangqian, L.1    Sidiropoulos, N.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.