A comparison of algorithms for fitting the PARAFAC model

Computational Statistics and Data Analysis - Tập 50 Số 7 - Trang 1700-1734 - 2006
Giorgio Tomasi1, Rasmus Bro1
1Food Science, Royal Veterinary and Agricultural University, Rolighedsvej 30, DK-1958 Frederiksberg C, Denmark

Tóm tắt

Từ khóa


Tài liệu tham khảo

Andersson, 2000, The N-way Toolbox for MATLAB, Chemometrics Intell. Lab. Systems, 52, 1, 10.1016/S0169-7439(00)00071-X

Baunsgaard, 2000, Analysis of the effect of crystal size and color distribution on fluorescence measurements of solid sugar using chemometrics, Appl. Spectrosc., 54, 1684, 10.1366/0003702001948727

Björck, 1996

Bro, 1998

Bro, 1998, Improving the speed of multiway algorithms part II, Compression. Chemometrics Intell. Lab. Systems, 42, 105, 10.1016/S0169-7439(98)00011-2

Bro, 2003, A new efficient method for determining the number of components in PARAFAC models, J. Chemometrics, 17, 274, 10.1002/cem.801

Carroll, 1970, Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart–Young decomposition, Psychometrika, 35, 283, 10.1007/BF02310791

Carroll, 1980, Candelinc—a general-approach to multidimensional-analysis of many-way arrays with linear constraints on parameters, Psychometrika, 45, 3, 10.1007/BF02293596

Chen, 2000, A novel trilinear decomposition algorithm for second-order linear calibration, Chemometrics Intell. Lab. Systems, 52, 75, 10.1016/S0169-7439(00)00081-2

Chen, 2001, Pseudo alternating least squares algorithm for trilinear decomposition, J. Chemometrics, 15, 149, 10.1002/cem.630

Faber, 2003, Recent developments in CANDECOMP/PARAFAC algorithms, Chemometrics Intell. Lab. Systems, 65, 119, 10.1016/S0169-7439(02)00089-8

Golub, 1996

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.

Hayashi, 1982, A new algorithm to solve PARAFAC-model, Behaviormetrika, 11, 49, 10.2333/bhmk.9.11_49

Ho, 1978, Application of method of rank annihilation to quantitative-analyses of multicomponent fluorescence data from video fluorometer, Anal. Chem., 50, 1108, 10.1021/ac50030a026

Ho, 1980, Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic-hydrocarbons, Anal. Chem., 52, 1071, 10.1021/ac50057a018

Ho, 1981, Simultaneous multicomponent rank annihilation and applications to multicomponent fluorescent data acquired by the video fluorometer, Anal. Chem., 53, 92, 10.1021/ac00224a024

Hopke, 1998, Three-way (PARAFAC) factor analysis, Chemometrics Intell. Lab. Systems, 43, 25, 10.1016/S0169-7439(98)00077-X

Jiang, 1999, Alternating coupled vectors resolution (ACOVER) method for trilinear analysis of three-way data, J. Chemometrics, 13, 557, 10.1002/(SICI)1099-128X(199911/12)13:6<557::AID-CEM563>3.0.CO;2-C

Jiang, 2000, Three-way data resolution by alternating slice-wise diagonalization (ASD) method, J. Chemometrics, 14, 15, 10.1002/(SICI)1099-128X(200001/02)14:1<15::AID-CEM571>3.0.CO;2-Z

Kiers, 1998, A three-step algorithm for CANDECOMP/PARAFAC analysis of large data sets with multicollinearity, J. Chemometrics, 12, 155, 10.1002/(SICI)1099-128X(199805/06)12:3<155::AID-CEM502>3.0.CO;2-5

Kiers, 1999, PARAFAC2—Part I, A direct fitting algorithm for the PARAFAC2 model. J. Chemometrics, 13, 275

Krijnen, 1993

Kruskal, 1989, How (MFA) data can cause degenerate PARAFAC solutions, among other relationships, 115

Levenberg, 1944, A method for the solution of certain problems in least squares, Quart. Appl. Math., 2, 164, 10.1090/qam/10666

Li, 2000, Alternating coupled matrices resolution method for three-way arrays analysis, Chemometrics Intell. Lab. Systems, 52, 33, 10.1016/S0169-7439(00)00073-3

Liu, 2001, Cramer–Rao lower bounds for low-rank decomposition of multidimensional arrays, IEEE Trans. Signal Process., 49, 2074, 10.1109/78.942635

Lorber, 1985, Features of quantifying chemical-composition from two-dimensional data array by the rank annihilation factor-analysis method, Anal. Chem., 57, 2395, 10.1021/ac00289a052

Madsen, 2004

Magnus, 1999

Marquadt, 1963, An Algorithm for least-squares estimation of nonlinear parameters, SIAM J. Appl. Math., 11, 431, 10.1137/0111030

MATLAB 6.5, The Mathworks, www.themathworks.com.

Mitchell, 1994, Slowly converging parafac sequences—swamps and 2-Factor degeneracies, J. Chemometrics, 8, 155, 10.1002/cem.1180080207

Paatero, 1997, A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis, Chemometrics Intell. Lab. Systems, 38, 223, 10.1016/S0169-7439(97)00031-2

Paatero, 2000, Construction and analysis of degenerate PARAFAC models, J. Chemometrics, 14, 285, 10.1002/1099-128X(200005/06)14:3<285::AID-CEM584>3.0.CO;2-1

Rao, 1971

Rayens, 1997, Two-factor degeneracies and a stabilization of PARAFAC, Chemometrics Intell. Lab. Systems, 38, 173, 10.1016/S0169-7439(97)00033-6

Riu, 2003, Jack-knife technique for outlier detection and estimation of standard errors in PARAFAC models, Chemometrics Intell. Lab. Systems, 65, 35, 10.1016/S0169-7439(02)00090-4

Sanchez, 1986, Generalized rank annihilation factor-analysis, Anal. Chem., 58, 496, 10.1021/ac00293a054

Sanchez, 1990, Tensorial resolution, J. Chemometrics, 4, 29, 10.1002/cem.1180040105

Sidiropoulos, 2000, On the uniqueness of multilinear decomposition of N-way arrays, J. Chemometrics, 14, 229, 10.1002/1099-128X(200005/06)14:3<229::AID-CEM587>3.0.CO;2-N

Tomasi, G., Bro, R., 2004. PARAFAC and missing values. Chemometrics Intell. Lab. Systems, in press.

Wu, 1998, An alternating trilinear decomposition algorithm with application to calibration of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons, J. Chemometrics, 12, 1, 10.1002/(SICI)1099-128X(199801/02)12:1<1::AID-CEM492>3.0.CO;2-4

Yates, 1933, The analysis of replicated experiments when the field results are incomplete, Empire J. Exp. Agri., 1, 129