메뉴 건너뛰기




Volumn 294, Issue 1-3, 1999, Pages 169-179

Simplicity of core arrays in three-way principal component analysis and the typical rank of p × q × 2 arrays 2606

Author keywords

Candecomp; Core arrays; Parafac; Simple structure; Three mode principal component analysis; Three way rank; Typical tensorial rank

Indexed keywords


EID: 0041595584     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00057-9     Document Type: Article
Times cited : (54)

References (22)
  • 1
    • 21144478327 scopus 로고
    • Maximal rank of an element of a tensor product
    • R.A Bailey, C.A. Rowley, Maximal rank of an element of a tensor product, Linear Algebra and Appl. 182 (1993) 1-7.
    • (1993) Linear Algebra and Appl. , vol.182 , pp. 1-7
    • Bailey, R.A.1    Rowley, C.A.2
  • 3
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart Young decomposition
    • J.D. Carroll, J.J. Chang, 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
  • 6
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Models and conditions for an explanatory multi-modal factor analysis
    • R.A. Harshman, Foundations of the PARAFAC procedure: models and conditions for an explanatory multi-modal factor analysis. University of California at Los Angeles, UCLA Working Papers in Phonetics 16 (1970) 1-84.
    • (1970) University of California at Los Angeles, UCLA Working Papers in Phonetics , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 7
    • 1642323297 scopus 로고
    • Optimal evaluation of a pair of bilinear forms
    • J. Ja'Ja', Optimal evaluation of a pair of bilinear forms, SIAM J. on Computing 8 (3) (1979) 281-293.
    • (1979) SIAM J. on Computing , vol.8 , Issue.3 , pp. 281-293
    • Ja'Ja', J.1
  • 8
    • 0001019769 scopus 로고
    • Tuckals core rotations and constrained TUCKALS modelling
    • H.A.L. Kiers, Tuckals core rotations and constrained TUCKALS modelling, Statistica Applicata 4 (1992) 659-667.
    • (1992) Statistica Applicata , vol.4 , pp. 659-667
    • Kiers, H.A.L.1
  • 9
    • 0031322119 scopus 로고    scopus 로고
    • Three-mode orthomax rotation
    • H.A.L. Kiers, Three-mode orthomax rotation, Psychometrika 62 (1997) 579-598.
    • (1997) Psychometrika , vol.62 , pp. 579-598
    • Kiers, H.A.L.1
  • 10
    • 0010747553 scopus 로고    scopus 로고
    • Recent developments in three-mode factor analysis: Constrained three-mode factor analysis and core rotations
    • C. Hayashi, N. Ohsumi, K. Yajima, Y. Tanaka, H.H. Bock, Y. Baba (Eds.), Springer, Tokyo
    • H.A.L. Kiers, Recent developments in three-mode factor analysis: Constrained three-mode factor analysis and core rotations. In: C. Hayashi, N. Ohsumi, K. Yajima, Y. Tanaka, H.H. Bock, Y. Baba (Eds.), Data Science, Classification, and Related Methods, Springer, Tokyo, 1998, pp. 563-574.
    • (1998) Data Science, Classification, and Related Methods , pp. 563-574
    • Kiers, H.A.L.1
  • 11
    • 0032483290 scopus 로고    scopus 로고
    • Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure
    • H.A.L. Kiers, Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure, Computational Statistics and Data Analysis 28 (1998) 307-324.
    • (1998) Computational Statistics and Data Analysis , vol.28 , pp. 307-324
    • Kiers, H.A.L.1
  • 12
    • 0031477528 scopus 로고    scopus 로고
    • Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case
    • H.A.L. Kiers, J.M.F. Ten Berge, R. Rocci, Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case, Psychometrika 62 (1997) 349-374.
    • (1997) Psychometrika , vol.62 , pp. 349-374
    • Kiers, H.A.L.1    Ten Berge, J.M.F.2    Rocci, R.3
  • 13
    • 0002332422 scopus 로고
    • Principal component analysis of three-mode data by means of alternating least-squares algorithms
    • P.M. Kroonenberg, J. De Leeuw, Principal component analysis of three-mode data by means of alternating least-squares algorithms, Psychometrika 45 (1980) 69-97.
    • (1980) Psychometrika , vol.45 , pp. 69-97
    • Kroonenberg, P.M.1    De Leeuw, J.2
  • 14
    • 48749101457 scopus 로고
    • Three-way arrays: Rank and uniqueness of trilinear decompositions with applications to arithmetic complexity and statistics
    • J.B. Kruskal, Three-way arrays: Rank and uniqueness of trilinear decompositions with applications to arithmetic complexity and statistics, Linear Algebra and Appl. 18 (1977) 95-138.
    • (1977) Linear Algebra and Appl. , vol.18 , pp. 95-138
    • Kruskal, J.B.1
  • 16
    • 0001837391 scopus 로고
    • Rank, decomposition, and uniqueness for 3-way and N-way arrays
    • R. Coppi and S. Bolasco (Eds.), North-Holland, Amsterdam
    • J.B. Kruskal, Rank, decomposition, and uniqueness for 3-way and N-way arrays. In: R. Coppi and S. Bolasco (Eds.), Multiway Data Analysis, North-Holland, Amsterdam, 1989.
    • (1989) Multiway Data Analysis
    • Kruskal, J.B.1
  • 18
    • 0032345550 scopus 로고    scopus 로고
    • A case of extreme simplicity of the core matrix in three-mode principal components analysis
    • T. Murakami, J.M.F. Ten Berge, H.A.L. Kiers, A case of extreme simplicity of the core matrix in three-mode principal components analysis, Psychometrika 63 (1998) 255-261.
    • (1998) Psychometrika , vol.63 , pp. 255-261
    • Murakami, T.1    Ten Berge, J.M.F.2    Kiers, H.A.L.3
  • 19
    • 51249165392 scopus 로고
    • Three-mode factor analysis with binary core and orthonormality constraints
    • R. Rocci, Three-mode factor analysis with binary core and orthonormality constraints, J. Italian Stat. Society 2 (1992) 413-422.
    • (1992) J. Italian Stat. Society , vol.2 , pp. 413-422
    • Rocci, R.1
  • 20
    • 0000020580 scopus 로고
    • Kruskal's polynomial for 2 × 2 × 2 arrays and a generalization to 2 × n × n arrays
    • J.M.F. Ten Berge, Kruskal's polynomial for 2 × 2 × 2 arrays and a generalization to 2 × n × n arrays, Psychometrika 56 (1991) 631-636.
    • (1991) Psychometrika , vol.56 , pp. 631-636
    • Ten Berge, J.M.F.1
  • 21
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • L.R. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika 31 (1966) 279-311.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 22
    • 44949289634 scopus 로고
    • Maximal bilinear complexity and codes
    • J. Von zur Gathen, Maximal bilinear complexity and codes, Linear Algebra and Appl. 144 (1991) 49-61.
    • (1991) Linear Algebra and Appl. , vol.144 , pp. 49-61
    • Von Zur Gathen, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.