메뉴 건너뛰기




Volumn 18, Issue 1, 2004, Pages 17-21

Simplicity and typical rank of three-way arrays, with applications to Tucker-3 analysis with simple cores

Author keywords

CANDECOMP PARAFAC; Constrained tucker models; Uniqueness

Indexed keywords

CANDECOMP/PARAFAC; CHEMOMETRICES; CONSTRAINED TUCK MODEL; SIMPLE++; THREE-WAY ARRAYS; THREE-WAY PRINCIPAL COMPONENT ANALYSIS; UNIQUENESS;

EID: 2642560409     PISSN: 08869383     EISSN: None     Source Type: Journal    
DOI: 10.1002/cem.840     Document Type: Conference Paper
Times cited : (18)

References (24)
  • 1
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition
    • Carroll JD, Chang JJ. Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition. Psychometrika 1970; 35: 283-319.
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carroll, J.D.1    Chang, J.J.2
  • 2
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Models and conditions for an 'explanatory' multi-mode factor analysis
    • Harshman RA. Foundations of the PARAFAC procedure: models and conditions for an 'explanatory' multi-mode factor analysis. UCLA Working Papers Phonet. 1970; 16: 1-84.
    • (1970) UCLA Working Papers Phonet , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 3
    • 0002740439 scopus 로고
    • Determination and proof of minimum uniqueness conditions for PARAFAC1
    • Harshman RA. Determination and proof of minimum uniqueness conditions for PARAFAC1. UCLA Working Papers Phonet. 1972; 22: 111-117.
    • (1972) UCLA Working Papers Phonet , vol.22 , pp. 111-117
    • Harshman, R.A.1
  • 4
    • 48749101457 scopus 로고
    • Three-way arrays: Rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics
    • Kruskal JB. Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics. Linear Algebra Appl. 1977; 18: 95-138.
    • (1977) Linear Algebra Appl. , vol.18 , pp. 95-138
    • Kruskal, J.B.1
  • 5
    • 0033653594 scopus 로고    scopus 로고
    • On the uniqueness of multilinear decomposition of N-way arrays
    • Sidiropoulos ND, Bro R. On the uniqueness of multilinear decomposition of N-way arrays. J. Chemometrics 2000; 14: 229-239.
    • (2000) J. Chemometrics , vol.14 , pp. 229-239
    • Sidiropoulos, N.D.1    Bro, R.2
  • 7
    • 0013953617 scopus 로고
    • Some mathematical notes on three-mode factor analysis
    • Tucker LR. Some mathematical notes on three-mode factor analysis. Psychometrika 1966; 31: 279-311.
    • (1966) Psychometrika , vol.31 , pp. 279-311
    • Tucker, L.R.1
  • 8
    • 0002332422 scopus 로고
    • Principal component analysis of three-mode data by means of alternating least-squares
    • Kroonenberg PM, De Leeuw J. Principal component analysis of three-mode data by means of alternating least-squares. Psychometrika 1980; 45: 69-97.
    • (1980) Psychometrika , vol.45 , pp. 69-97
    • Kroonenberg, P.M.1    De Leeuw, J.2
  • 9
    • 0036746470 scopus 로고    scopus 로고
    • Transforming three-way arrays to maximal simplicity
    • Rocci R, ten Berge JMF. Transforming three-way arrays to maximal simplicity. Psychometrika 2002; 67: 351-365.
    • (2002) Psychometrika , vol.67 , pp. 351-365
    • Rocci, R.1    Ten Berge, J.M.F.2
  • 10
    • 0031477528 scopus 로고    scopus 로고
    • Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case
    • Kiers HAL, ten Berge JMF, Rocci R. Uniqueness of three-mode factor models with sparse cores: the 3 × 3 × 3 case. Psychometrika 1997; 62: 349-374.
    • (1997) Psychometrika , vol.62 , pp. 349-374
    • Kiers, H.A.L.1    Ten Berge, J.M.F.2    Rocci, R.3
  • 11
    • 0035541139 scopus 로고    scopus 로고
    • Multidimensional association models. A multilinear approach
    • Wong RS-K. Multidimensional association models. A multilinear approach. Sociol Methods Res 2001; 30: 197-240.
    • (2001) Sociol Methods Res , vol.30 , pp. 197-240
    • Wong, R.S.-K.1
  • 13
    • 0001615008 scopus 로고    scopus 로고
    • Constrained three-mode factor analysis as a tool for parameter estimation with second-order instrumental data
    • Kiers HAL, Smilde AK. Constrained three-mode factor analysis as a tool for parameter estimation with second-order instrumental data. J. Chemometrics 1998; 12: 125-147.
    • (1998) J. Chemometrics , vol.12 , pp. 125-147
    • Kiers, H.A.L.1    Smilde, A.K.2
  • 14
    • 0035117034 scopus 로고    scopus 로고
    • Modeling of spectroscopic batch process data using grey models to incorporate external information
    • Gurden SP, Westerhuis JA, Bijlsma S, Smilde A. Modeling of spectroscopic batch process data using grey models to incorporate external information. J. Chemometrics 2001; 15: 101-121.
    • (2001) J. Chemometrics , vol.15 , pp. 101-121
    • Gurden, S.P.1    Westerhuis, J.A.2    Bijlsma, S.3    Smilde, A.4
  • 15
    • 0036934940 scopus 로고    scopus 로고
    • Non-triviality and identification of a constrained Tucker3 analysis
    • Ten Berge JMF, Smilde AK. Non-triviality and identification of a constrained Tucker3 analysis. J. Chemometrics 2002; 16: 609-612.
    • (2002) J. Chemometrics , vol.16 , pp. 609-612
    • Ten Berge, J.M.F.1    Smilde, A.K.2
  • 16
    • 0032483290 scopus 로고    scopus 로고
    • Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure
    • Kiers HAL. Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure. Comput. Statist. Data Anal. 1998; 28: 307-324.
    • (1998) Comput. Statist. Data Anal. , vol.28 , pp. 307-324
    • Kiers, H.A.L.1
  • 18
    • 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 JMF, Kiers HAL. Simplicity of core arrays in three-way principal component analysis and the typical rank of P × Q × 2 arrays. Linear Algebra Appl. 1999; 294: 169-179.
    • (1999) Linear Algebra Appl. , vol.294 , pp. 169-179
    • Ten Berge, J.M.F.1    Kiers, H.A.L.2
  • 19
    • 0032345550 scopus 로고    scopus 로고
    • A case of extreme simplicity of the core matrix in three-mode principal components analysis
    • Murakami T, ten Berge JMF, Kiers HAL. A case of extreme simplicity of the core matrix in three-mode principal components analysis. Psychometrika 1998; 63: 255-261.
    • (1998) Psychometrika , vol.63 , pp. 255-261
    • Murakami, T.1    Ten Berge, J.M.F.2    Kiers, H.A.L.3
  • 20
    • 0001837391 scopus 로고
    • Rank, decomposition, and uniqueness for 3-way and N-way arrays
    • Coppi R, Bolasco S (eds). Elsevier: Amsterdam
    • Kruskal JB. Rank, decomposition, and uniqueness for 3-way and N-way arrays. In Multiway Data Analysis, Coppi R, Bolasco S (eds). Elsevier: Amsterdam, 1989; 7-18.
    • (1989) Multiway Data Analysis , pp. 7-18
    • Kruskal, J.B.1
  • 21
    • 0034559666 scopus 로고    scopus 로고
    • The typical rank of tall three-way arrays
    • Ten Berge JMF. The typical rank of tall three-way arrays. Psychometrika 2000; 65: 525-532.
    • (2000) Psychometrika , vol.65 , pp. 525-532
    • Ten Berge, J.M.F.1
  • 22
    • 2642580865 scopus 로고    scopus 로고
    • Partial uniqueness in CANDECOMP/PARAFAC
    • Ten Berge JMF. Partial uniqueness in CANDECOMP/PARAFAC. J. Chemometrics 2004; 18: 12-16.
    • (2004) J. Chemometrics , vol.18 , pp. 12-16
    • Ten Berge, J.M.F.1
  • 23
    • 85153551386 scopus 로고    scopus 로고
    • Typical rank and INDSCAL dimensionality for symmetric arrays of order I × 2 × 2 or I × 3 × 3
    • in press
    • Ten Berge JMF, Sidiropoulos ND, Rocci R. Typical rank and INDSCAL dimensionality for symmetric arrays of order I × 2 × 2 or I × 3 × 3. Linear Algebra Appl (in press).
    • Linear Algebra Appl.
    • Ten Berge, J.M.F.1    Sidiropoulos, N.D.2    Rocci, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.