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Volumn 418, Issue 1, 2006, Pages 215-224

Symmetry transformations for square sliced three-way arrays, with applications to their typical rank

Author keywords

Candecomp; Indscal; Parafac; Three mode component analysis; Three way rank; Typical tensorial rank

Indexed keywords

ARRAYS; COMPUTABILITY AND DECIDABILITY; LINEAR ALGEBRA; NUMERICAL METHODS; STATISTICAL METHODS;

EID: 33747839474     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.02.002     Document Type: Article
Times cited : (11)

References (18)
  • 2
    • 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
  • 4
    • 33747850286 scopus 로고    scopus 로고
    • R.L. 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, vol. 16, 1970, pp. 1-84. Available from: .
  • 5
    • 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
  • 6
    • 33747815430 scopus 로고    scopus 로고
    • J.B. Kruskal, Statement of some current results about three-way arrays, Unpublished report, 1983.
  • 7
    • 0001837391 scopus 로고
    • Rank, decomposition, and uniqueness for 3-way and N-way arrays
    • Coppi R., and Bolasco S. (Eds), North-Holland, Amsterdam
    • Kruskal J.B. Rank, decomposition, and uniqueness for 3-way and N-way arrays. In: Coppi R., and Bolasco S. (Eds). Multiway Data Analysis (1989), North-Holland, Amsterdam 7-18
    • (1989) Multiway Data Analysis , pp. 7-18
    • Kruskal, J.B.1
  • 8
    • 33747862322 scopus 로고    scopus 로고
    • J.B. Kruskal, The maximum rank of a 3 × 3 × 3 array, Unpublished communication, 1991.
  • 10
    • 33747861746 scopus 로고    scopus 로고
    • R. Rocci, Proof of the maximum rank of 3 × 3 × 3 arrays, Unpublished report, 1993.
  • 11
    • 0036746470 scopus 로고    scopus 로고
    • Transforming three-way arrays to maximal simplicity
    • Rocci R., and Ten Berge J.M.F. Transforming three-way arrays to maximal simplicity. Psychometrika 67 (2002) 351-365
    • (2002) Psychometrika , vol.67 , pp. 351-365
    • Rocci, R.1    Ten Berge, J.M.F.2
  • 12
    • 0000020580 scopus 로고
    • Kruskal's polynomial for 2 × 2 × 2 arrays and a generalization to 2 × n × n arrays
    • Ten Berge J.M.F. 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
  • 13
    • 0034559666 scopus 로고    scopus 로고
    • The typical rank of tall three-way arrays
    • Ten Berge J.M.F. The typical rank of tall three-way arrays. Psychometrika 65 (2000) 525-532
    • (2000) Psychometrika , vol.65 , pp. 525-532
    • Ten Berge, J.M.F.1
  • 14
    • 2642580865 scopus 로고    scopus 로고
    • Partial uniqueness in Candecomp/Parafac
    • Ten Berge J.M.F. Partial uniqueness in Candecomp/Parafac. J. Chemometrics 18 (2004) 12-16
    • (2004) J. Chemometrics , vol.18 , pp. 12-16
    • Ten Berge, J.M.F.1
  • 15
    • 0041595584 scopus 로고    scopus 로고
    • Simplicity of core arrays in three-way principal component analysis and the typical rank of P × Q × 2 arrays
    • Ten Berge J.M.F., and Kiers H.A.L. Simplicity of core arrays in three-way principal component analysis and the typical rank of P × Q × 2 arrays. Linear Algebra Appl. 294 (1999) 169-179
    • (1999) Linear Algebra Appl. , vol.294 , pp. 169-179
    • Ten Berge, J.M.F.1    Kiers, H.A.L.2
  • 16
    • 3142774353 scopus 로고    scopus 로고
    • Typical rank and INDSCAL dimensionality for symmetric 3-way arrays of order I × 2 × 2 and I × 3 × 3
    • Ten Berge J.M.F., Sidiropoulos N.D., and Rocci R. Typical rank and INDSCAL dimensionality for symmetric 3-way arrays of order I × 2 × 2 and 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
  • 17
    • 0036934940 scopus 로고    scopus 로고
    • Non-triviality and identification of a constrained Tucker3 analysis
    • Ten Berge J.M.F., and Smilde A.K. Non-triviality and identification of a constrained Tucker3 analysis. J. Chemometrics 16 (2002) 609-612
    • (2002) J. Chemometrics , vol.16 , pp. 609-612
    • Ten Berge, J.M.F.1    Smilde, A.K.2
  • 18
    • 0013953617 scopus 로고
    • Some mathematical notes on three-way factor analysis
    • Tucker L.R. Some mathematical notes on three-way factor analysis. Psychometrika 31 (1966) 279-311
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.