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Volumn 431, Issue 1-2, 2009, Pages 211-227

On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode

Author keywords

Candecomp; Indscal; Parafac; Three way arrays; Uniqueness

Indexed keywords

CANDECOMP; INDSCAL; PARAFAC; THREE-WAY ARRAYS; UNIQUENESS;

EID: 65049083795     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.02.025     Document Type: Article
Times cited : (48)

References (26)
  • 1
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition
    • Carroll J.D., and Chang J.J. Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika 35 (1970) 283-319
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carroll, J.D.1    Chang, J.J.2
  • 2
    • 33746356349 scopus 로고    scopus 로고
    • A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization
    • De Lathauwer L. A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization. SIAM J. Matrix Anal. Appl. 28 (2006) 642-666
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 642-666
    • De Lathauwer, L.1
  • 3
    • 55349142218 scopus 로고    scopus 로고
    • Tensor rank and the ill-posedness of the best low-rank approximation problem
    • De Silva V., and Lim L.-H. Tensor rank and the ill-posedness of the best low-rank approximation problem. SIAM J. Matrix Anal. Appl. 30 (2008) 1084-1127
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 1084-1127
    • De Silva, V.1    Lim, L.-H.2
  • 6
    • 4344616103 scopus 로고    scopus 로고
    • Kruskal's permutation lemma and the identification of Candecomp/Parafac and bilinear models with constant modulus constraints
    • Jiang T., and Sidiropoulos N.D. Kruskal's permutation lemma and the identification of Candecomp/Parafac and bilinear models with constant modulus constraints. IEEE Trans. Signal Process. 52 (2004) 2625-2636
    • (2004) IEEE Trans. Signal Process. , vol.52 , pp. 2625-2636
    • Jiang, T.1    Sidiropoulos, N.D.2
  • 7
    • 85047681558 scopus 로고    scopus 로고
    • Three-way component analysis: principles and illustrative application
    • Kiers H.A.L., and Van Mechelen I. Three-way component analysis: principles and illustrative application. Psychol. Methods 6 (2001) 84-110
    • (2001) Psychol. Methods , vol.6 , pp. 84-110
    • Kiers, H.A.L.1    Van Mechelen, I.2
  • 9
    • 52949104087 scopus 로고    scopus 로고
    • On the non-existence of optimal solutions and the occurrence of "degeneracy in the Candecomp/Parafac model
    • Krijnen W.P., Dijkstra T.K., and Stegeman A. On the non-existence of optimal solutions and the occurrence of "degeneracy in the Candecomp/Parafac model. Psychometrika 73 (2008) 431-439
    • (2008) Psychometrika , vol.73 , pp. 431-439
    • Krijnen, W.P.1    Dijkstra, T.K.2    Stegeman, A.3
  • 11
    • 48749101457 scopus 로고
    • Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics
    • Kruskal J.B. Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics. Linear Algebra Appl. 18 (1977) 95-138
    • (1977) Linear Algebra Appl. , vol.18 , pp. 95-138
    • Kruskal, J.B.1
  • 12
    • 0003052447 scopus 로고
    • How 3-MFA data can cause degenerate Parafac solutions, among other relationships
    • R. Coppi, S. Bolasco Eds, North-Holland
    • J.B. Kruskal, R.A. Harshman, M.E. Lundy, How 3-MFA data can cause degenerate Parafac solutions, among other relationships, in: R. Coppi, S. Bolasco (Eds.), Multiway Data Analysis, North-Holland, 1989, pp. 115-121.
    • (1989) Multiway Data Analysis , pp. 115-121
    • Kruskal, J.B.1    Harshman, R.A.2    Lundy, M.E.3
  • 13
    • 0033653594 scopus 로고    scopus 로고
    • On the uniqueness of multilinear decomposition of N-way arrays
    • Sidiropoulos N.D., and Bro R. On the uniqueness of multilinear decomposition of N-way arrays. J. Chemometrics 14 (2000) 229-239
    • (2000) J. Chemometrics , vol.14 , pp. 229-239
    • Sidiropoulos, N.D.1    Bro, R.2
  • 17
    • 33751214191 scopus 로고    scopus 로고
    • 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 71 (2006) 483-501
    • (2006) Psychometrika , vol.71 , pp. 483-501
    • Stegeman, A.1
  • 18
    • 38949176012 scopus 로고    scopus 로고
    • 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 72 (2007) 601-619
    • (2007) Psychometrika , vol.72 , pp. 601-619
    • Stegeman, A.1
  • 19
    • 52949146687 scopus 로고    scopus 로고
    • 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. 30 (2008) 988-1007
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 988-1007
    • Stegeman, A.1
  • 20
    • 24644469120 scopus 로고    scopus 로고
    • Kruskal's condition for uniqueness in Candecomp/Parafac when ranks and k-ranks coincide
    • Stegeman A., and Ten Berge J.M.F. Kruskal's condition for uniqueness in Candecomp/Parafac when ranks and k-ranks coincide. Comput. Statist. Data Anal. 50 (2006) 210-220
    • (2006) Comput. Statist. Data Anal. , vol.50 , pp. 210-220
    • Stegeman, A.1    Ten Berge, J.M.F.2
  • 21
    • 33746359652 scopus 로고    scopus 로고
    • Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
    • Stegeman A., Ten Berge J.M.F., and De Lathauwer L. Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices. Psychometrika 71 (2006) 219-229
    • (2006) Psychometrika , vol.71 , pp. 219-229
    • Stegeman, A.1    Ten Berge, J.M.F.2    De Lathauwer, L.3
  • 22
    • 33750991900 scopus 로고    scopus 로고
    • On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
    • Stegeman A., and Sidiropoulos N.D. On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition. Linear Algebra Appl. 420 (2007) 540-552
    • (2007) Linear Algebra Appl. , vol.420 , pp. 540-552
    • Stegeman, A.1    Sidiropoulos, N.D.2
  • 23
    • 0039198932 scopus 로고
    • Some clarifications of the Candecomp algorithm applied to Indscal
    • Ten Berge J.M.F., and Kiers H.A.L. Some clarifications of the Candecomp algorithm applied to Indscal. Psychometrika 56 (1991) 317-326
    • (1991) Psychometrika , vol.56 , pp. 317-326
    • Ten Berge, J.M.F.1    Kiers, H.A.L.2
  • 25
    • 3142774353 scopus 로고    scopus 로고
    • Typical rank and Indscal dimensionality for symmetric three-way arrays of order I × 2 × 2 or I × 3 × 3
    • Ten Berge J.M.F., Sidiropoulos N.D., and Rocci R. Typical rank and Indscal dimensionality for symmetric three-way arrays of order I × 2 × 2 or I × 3 × 3. Linear Algebra Appl. 388 (2004) 363-377
    • (2004) Linear Algebra Appl. , vol.388 , pp. 363-377
    • Ten Berge, J.M.F.1    Sidiropoulos, N.D.2    Rocci, R.3
  • 26
    • 30144444694 scopus 로고    scopus 로고
    • A Comparison of algorithms for fitting the Parafac model
    • Tomasi G., and Bro R. A Comparison of algorithms for fitting the Parafac model. Comput. Statist. Data Anal. 50 (2006) 1700-1734
    • (2006) Comput. Statist. Data Anal. , vol.50 , pp. 1700-1734
    • Tomasi, G.1    Bro, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.