메뉴 건너뛰기




Volumn 50, Issue 7, 2006, Pages 1700-1734

A comparison of algorithms for fitting the PARAFAC model

Author keywords

ALS; Levenberg Marquadt; PARAFAC; PMF3; SWATLD

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FLUORESCENCE; ITERATIVE METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING;

EID: 30144444694     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2004.11.013     Document Type: Article
Times cited : (341)

References (44)
  • 2
    • 0034314693 scopus 로고    scopus 로고
    • Analysis of the effect of crystal size and color distribution on fluorescence measurements of solid sugar using chemometrics
    • D. Baunsgaard, L. Munck, and L. Norgaard Analysis of the effect of crystal size and color distribution on fluorescence measurements of solid sugar using chemometrics Appl. Spectrosc. 54 11 2000 1684 1689
    • (2000) Appl. Spectrosc. , vol.54 , Issue.11 , pp. 1684-1689
    • Baunsgaard, D.1    Munck, L.2    Norgaard, L.3
  • 3
    • 0003852590 scopus 로고    scopus 로고
    • First ed Society for Industrial and Applied Mathematics Philadelphia, PA, USA
    • Å. Björck Numerical Methods for Least Squares Problems First ed 1996 Society for Industrial and Applied Mathematics Philadelphia, PA, USA
    • (1996) Numerical Methods for Least Squares Problems
    • Björck, Å.1
  • 4
  • 6
    • 0038685059 scopus 로고    scopus 로고
    • A new efficient method for determining the number of components in PARAFAC models
    • R. Bro, and H.A.L. Kiers A new efficient method for determining the number of components in PARAFAC models J. Chemometrics 17 5 2003 274 286
    • (2003) J. Chemometrics , vol.17 , Issue.5 , pp. 274-286
    • Bro, R.1    Kiers, H.A.L.2
  • 7
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition
    • J.D. Carroll, and J.J. Chang Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition Psychometrika 35 3 1970 283 319
    • (1970) Psychometrika , vol.35 , Issue.3 , pp. 283-319
    • Carroll, J.D.1    Chang, J.J.2
  • 8
    • 34250252877 scopus 로고
    • Candelinc - A general-approach to multidimensional-analysis of many-way arrays with linear constraints on parameters
    • J.D. Carroll, S. Pruzansky, and J.B. Kruskal Candelinc - a general-approach to multidimensional-analysis of many-way arrays with linear constraints on parameters Psychometrika 45 1 1980 3 24
    • (1980) Psychometrika , vol.45 , Issue.1 , pp. 3-24
    • Carroll, J.D.1    Pruzansky, S.2    Kruskal, J.B.3
  • 9
    • 0034648456 scopus 로고    scopus 로고
    • A novel trilinear decomposition algorithm for second-order linear calibration
    • Z.P. Chen, H.L. Wu, J.H. Jiang, Y. Li, and R.Q. Yu A novel trilinear decomposition algorithm for second-order linear calibration Chemometrics Intell. Lab. Systems 52 1 2000 75 86
    • (2000) Chemometrics Intell. Lab. Systems , vol.52 , Issue.1 , pp. 75-86
    • Chen, Z.P.1    Wu, H.L.2    Jiang, J.H.3    Li, Y.4    Yu, R.Q.5
  • 10
    • 0035106980 scopus 로고    scopus 로고
    • Pseudo alternating least squares algorithm for trilinear decomposition
    • Z.P. Chen, Y. Li, and R.Q. Yu Pseudo alternating least squares algorithm for trilinear decomposition J. Chemometrics 15 3 2001 149 167
    • (2001) J. Chemometrics , vol.15 , Issue.3 , pp. 149-167
    • Chen, Z.P.1    Li, Y.2    Yu, R.Q.3
  • 11
    • 0037469083 scopus 로고    scopus 로고
    • Recent developments in CANDECOMP/PARAFAC algorithms: A critical review
    • N.M. Faber, R. Bro, and P.K. Hopke Recent developments in CANDECOMP/PARAFAC algorithms a critical review Chemometrics Intell. Lab. Systems 65 1 2003 119 137
    • (2003) Chemometrics Intell. Lab. Systems , vol.65 , Issue.1 , pp. 119-137
    • Faber, N.M.1    Bro, R.2    Hopke, P.K.3
  • 12
    • 0004236492 scopus 로고    scopus 로고
    • The Johns Hopkins University Press Baltimore, London
    • G.H. Golub, and C.F. Van Loan Matrix Computations 1996 The Johns Hopkins University Press Baltimore, London pp. 1-47
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 13
    • 0002740437 scopus 로고
    • Foundations of the PARAFAC procedure: Models and conditions for an 'explanatory' multi-modal factor analysis
    • Harshman, R.A., 1970. Foundations of the PARAFAC procedure: models and conditions for an 'explanatory' multi-modal factor analysis. UCLA working papers in phonetics, vol. 16, pp. 1-84.
    • (1970) UCLA Working Papers in Phonetics , vol.16 , pp. 1-84
    • Harshman, R.A.1
  • 14
    • 30144436073 scopus 로고
    • A new algorithm to solve PARAFAC-model
    • C. Hayashi, and F. Hayashi A new algorithm to solve PARAFAC-model Behaviormetrika 11 1982 49
    • (1982) Behaviormetrika , vol.11 , pp. 49
    • Hayashi, C.1    Hayashi, F.2
  • 15
    • 0017995905 scopus 로고
    • Application of method of rank annihilation to quantitative-analyses of multicomponent fluorescence data from video fluorometer
    • C.N. Ho, G.D. Christian, and E.R. Davidson Application of method of rank annihilation to quantitative-analyses of multicomponent fluorescence data from video fluorometer Anal. Chem. 50 8 1978 1108 1113
    • (1978) Anal. Chem. , vol.50 , Issue.8 , pp. 1108-1113
    • Ho, C.N.1    Christian, G.D.2    Davidson, E.R.3
  • 16
    • 0019025268 scopus 로고
    • Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic-hydrocarbons
    • C.N. Ho, G.D. Christian, and E.R. Davidson Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic-hydrocarbons Anal. Chem. 52 7 1980 1071 1079
    • (1980) Anal. Chem. , vol.52 , Issue.7 , pp. 1071-1079
    • Ho, C.N.1    Christian, G.D.2    Davidson, E.R.3
  • 17
    • 0019354253 scopus 로고
    • Simultaneous multicomponent rank annihilation and applications to multicomponent fluorescent data acquired by the video fluorometer
    • C.N. Ho, G.D. Christian, and E.R. Davidson Simultaneous multicomponent rank annihilation and applications to multicomponent fluorescent data acquired by the video fluorometer Anal. Chem. 53 1 1981 92 98
    • (1981) Anal. Chem. , vol.53 , Issue.1 , pp. 92-98
    • Ho, C.N.1    Christian, G.D.2    Davidson, E.R.3
  • 18
    • 0032575985 scopus 로고    scopus 로고
    • Three-way (PARAFAC) factor analysis: Examination and comparison of alternative computational methods as applied to ill-conditioned data
    • P.K. Hopke, P. Paatero, H. Jia, R.T. Ross, and R.A. Harshman Three-way (PARAFAC) factor analysis examination and comparison of alternative computational methods as applied to ill-conditioned data Chemometrics Intell. Lab. Systems 43 1-2 1998 25 42
    • (1998) Chemometrics Intell. Lab. Systems , vol.43 , Issue.1-2 , pp. 25-42
    • Hopke, P.K.1    Paatero, P.2    Jia, H.3    Ross, R.T.4    Harshman, R.A.5
  • 19
    • 0000985079 scopus 로고    scopus 로고
    • Alternating coupled vectors resolution (ACOVER) method for trilinear analysis of three-way data
    • J.H. Jiang, H.L. Wu, Y. Li, and R.Q. Yu Alternating coupled vectors resolution (ACOVER) method for trilinear analysis of three-way data J. Chemometrics 13 6 1999 557 578
    • (1999) J. Chemometrics , vol.13 , Issue.6 , pp. 557-578
    • Jiang, J.H.1    Wu, H.L.2    Li, Y.3    Yu, R.Q.4
  • 20
    • 0033671724 scopus 로고    scopus 로고
    • Three-way data resolution by alternating slice-wise diagonalization (ASD) method
    • J.H. Jiang, H.L. Wu, Y. Li, and R.Q. Yu Three-way data resolution by alternating slice-wise diagonalization (ASD) method J. Chemometrics 14 1 2000 15 36
    • (2000) J. Chemometrics , vol.14 , Issue.1 , pp. 15-36
    • Jiang, J.H.1    Wu, H.L.2    Li, Y.3    Yu, R.Q.4
  • 21
    • 0000925933 scopus 로고    scopus 로고
    • A three-step algorithm for CANDECOMP/PARAFAC analysis of large data sets with multicollinearity
    • H.A.L. Kiers A three-step algorithm for CANDECOMP/PARAFAC analysis of large data sets with multicollinearity J. Chemometrics 12 3 1998 155 171
    • (1998) J. Chemometrics , vol.12 , Issue.3 , pp. 155-171
    • Kiers, H.A.L.1
  • 24
    • 0003052447 scopus 로고
    • How (MFA) data can cause degenerate PARAFAC solutions, among other relationships
    • R. Coppi S. Bolasco Elsevier Science Publishers Amsterdam
    • J.B. Kruskal, R.A. Harshman, and M.E. Lundy How (MFA) data can cause degenerate PARAFAC solutions, among other relationships R. Coppi S. Bolasco Multiway Data Analysis 1989 Elsevier Science Publishers Amsterdam 115 122
    • (1989) Multiway Data Analysis , pp. 115-122
    • Kruskal, J.B.1    Harshman, R.A.2    Lundy, M.E.3
  • 25
    • 0000873069 scopus 로고
    • A method for the solution of certain problems in least squares
    • K. Levenberg A method for the solution of certain problems in least squares Quart. Appl. Math. 2 1944 164 168
    • (1944) Quart. Appl. Math. , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 26
    • 0034648381 scopus 로고    scopus 로고
    • Alternating coupled matrices resolution method for three-way arrays analysis
    • Y. Li, J.H. Jiang, H.L. Wu, Z.P. Chen, and R.Q. Yu Alternating coupled matrices resolution method for three-way arrays analysis Chemometrics Intell. Lab. Systems 52 1 2000 33 43
    • (2000) Chemometrics Intell. Lab. Systems , vol.52 , Issue.1 , pp. 33-43
    • Li, Y.1    Jiang, J.H.2    Wu, H.L.3    Chen, Z.P.4    Yu, R.Q.5
  • 27
    • 0035447407 scopus 로고    scopus 로고
    • Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays
    • X.Q. Liu, and N.D. Sidiropoulos Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays IEEE Trans. Signal Process. 49 9 2001 2074 2086
    • (2001) IEEE Trans. Signal Process. , vol.49 , Issue.9 , pp. 2074-2086
    • Liu, X.Q.1    Sidiropoulos, N.D.2
  • 28
    • 0001064966 scopus 로고
    • Features of quantifying chemical-composition from two-dimensional data array by the rank annihilation factor-analysis method
    • A. Lorber Features of quantifying chemical-composition from two-dimensional data array by the rank annihilation factor-analysis method Anal. Chem. 57 12 1985 2395 2397
    • (1985) Anal. Chem. , vol.57 , Issue.12 , pp. 2395-2397
    • Lorber, A.1
  • 31
    • 0000169232 scopus 로고
    • An Algorithm for least-squares estimation of nonlinear parameters
    • D. Marquadt An Algorithm for least-squares estimation of nonlinear parameters SIAM J. Appl. Math. 11 1963 431 441
    • (1963) SIAM J. Appl. Math. , vol.11 , pp. 431-441
    • Marquadt, D.1
  • 32
    • 1842516202 scopus 로고    scopus 로고
    • The Mathworks
    • MATLAB 6.5, The Mathworks, www.themathworks.com.
    • MATLAB 6.5
  • 33
    • 84984320741 scopus 로고
    • Slowly converging parafac sequences - Swamps and 2-Factor degeneracies
    • B.C. Mitchell, and D.S. Burdick Slowly converging parafac sequences - swamps and 2-Factor degeneracies J. Chemometrics 8 2 1994 155 168
    • (1994) J. Chemometrics , vol.8 , Issue.2 , pp. 155-168
    • Mitchell, B.C.1    Burdick, D.S.2
  • 34
    • 0030775193 scopus 로고    scopus 로고
    • A weighted non-negative least squares algorithm for three-way 'PARAFAC' factor analysis
    • P. Paatero A weighted non-negative least squares algorithm for three-way 'PARAFAC' factor analysis Chemometrics Intell. Lab. Systems 38 2 1997 223 242
    • (1997) Chemometrics Intell. Lab. Systems , vol.38 , Issue.2 , pp. 223-242
    • Paatero, P.1
  • 35
    • 0033653782 scopus 로고    scopus 로고
    • Construction and analysis of degenerate PARAFAC models
    • P. Paatero Construction and analysis of degenerate PARAFAC models J. Chemometrics 14 3 2000 285 299
    • (2000) J. Chemometrics , vol.14 , Issue.3 , pp. 285-299
    • Paatero, P.1
  • 37
    • 0030730107 scopus 로고    scopus 로고
    • Two-factor degeneracies and a stabilization of PARAFAC
    • W.S. Rayens, and B.C. Mitchell Two-factor degeneracies and a stabilization of PARAFAC Chemometrics Intell. Lab. Systems 38 2 1997 173 181
    • (1997) Chemometrics Intell. Lab. Systems , vol.38 , Issue.2 , pp. 173-181
    • Rayens, W.S.1    Mitchell, B.C.2
  • 38
    • 0037469085 scopus 로고    scopus 로고
    • Jack-knife technique for outlier detection and estimation of standard errors in PARAFAC models
    • J. Riu, and R. Bro Jack-knife technique for outlier detection and estimation of standard errors in PARAFAC models Chemometrics Intell. Lab. Systems 65 1 2003 35 49
    • (2003) Chemometrics Intell. Lab. Systems , vol.65 , Issue.1 , pp. 35-49
    • Riu, J.1    Bro, R.2
  • 39
    • 26444570774 scopus 로고
    • Generalized rank annihilation factor-analysis
    • E. Sanchez, and B.R. Kowalski Generalized rank annihilation factor-analysis Anal. Chem. 58 2 1986 496 499
    • (1986) Anal. Chem. , vol.58 , Issue.2 , pp. 496-499
    • Sanchez, E.1    Kowalski, B.R.2
  • 40
    • 85190314196 scopus 로고
    • Tensorial resolution: A direct trilinear decomposition
    • E. Sanchez, and B.R. Kowalski Tensorial resolution a direct trilinear decomposition J. Chemometrics 4 1990 29 45
    • (1990) J. Chemometrics , vol.4 , pp. 29-45
    • Sanchez, E.1    Kowalski, B.R.2
  • 41
    • 0033653594 scopus 로고    scopus 로고
    • On the uniqueness of multilinear decomposition of N-way arrays
    • N.D. Sidiropoulos, and R. Bro On the uniqueness of multilinear decomposition of N-way arrays J. Chemometrics 14 3 2000 229 239
    • (2000) J. Chemometrics , vol.14 , Issue.3 , pp. 229-239
    • Sidiropoulos, N.D.1    Bro, R.2
  • 43
    • 0002017118 scopus 로고    scopus 로고
    • An alternating trilinear decomposition algorithm with application to calibration of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons
    • H.L. Wu, M. Shibukawa, and K. Oguma An alternating trilinear decomposition algorithm with application to calibration of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons J. Chemometrics 12 1 1998 1 26
    • (1998) J. Chemometrics , vol.12 , Issue.1 , pp. 1-26
    • Wu, H.L.1    Shibukawa, M.2    Oguma, K.3
  • 44
    • 0000736815 scopus 로고
    • The analysis of replicated experiments when the field results are incomplete
    • F. Yates The analysis of replicated experiments when the field results are incomplete Empire J. Exp. Agri. 1 1933 129
    • (1933) Empire J. Exp. Agri. , vol.1 , pp. 129
    • Yates, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.