A weighted non-negative least squares algorithm for three-way 'PARAFAC' factor analysis

Chemometrics and Intelligent Laboratory Systems

Volumn 38, Issue 2, 1997, Pages 223-242

  Paatero, Pentti ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

CANDECOMP; Degeneracy; Multilinear models; Multiple solutions; PARAFAC; Positive matrix factorization

Indexed keywords

ALGORITHM; COMPUTER ANALYSIS; CONFERENCE PAPER; DATA ANALYSIS; FACTORIAL ANALYSIS; MATHEMATICAL MODEL; PHYSICS; PRIORITY JOURNAL;

EID: 0030775193     PISSN: 01697439     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0169-7439(97)00031-2     Document Type: Conference Paper

References (18)

1. R. Coppi, S. Bolasco (Eds.), Multiway Data Analysis, Elsevier, Amsterdam, 1989.
2. T. Wansbeek, J. Verhees, Models for multidimensional matrices in econometrics and psychometrics, in: R. Coppi, S. Bolasco (Eds.), Multiway Data Analysis, Elsevier, Amsterdam, 1989, pp. 543-552.
3. R.A. Harshman, M.E. Lundy, The PARAFAC model for three-way factor analysis and multidimensional scaling, in: Law et al. (Eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984, pp. 122-215.
4. R.T. Ross, S. Leurgans, Component resolution using multilinear models, Meth. Enzymol. 246 (1995) 679-700.
5. P. Paatero, U. Tapper, Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values, Environmetrics 5 (1994) 111-126.
6. R.A. Harshman, Foundations of the PARAFAC procedure, UCLA working papers in phonetics, Vol. 16, 1970, pp. 1-84, University Microfilms International No. 10,085.
7. P. Paatero, Least squares formulation of robust non-negative factor analysis, Chemometrics Intell. Lab. Syst. 37 (1997) 23-35.
8. J.M.F. ten Berge, Convergence of PARAFAC preprocessing procedures and the Deming-Stephan method of iterative proportional fitting, in: R. Coppi, S. Bolasco (Eds.), Multiway Data Analysis, Elsevier, Amsterdam, 1989, pp. 53-63.
9. P. Paatero, U. Tapper, Analysis of different modes of factor analysis as least squares fit problems, Chemometrics Intell. Lab. Syst. 18 (1993) 183-194.
10. B.C. Mitchell, D.S. Burdick, Slowly converging PARAFAC sequences: Swamps and two-factor degeneracies, J. Chemometrics 8 (1994) 155-168.
11. J.B. Kruskal, Three-way arrays: Rank and Uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics, Linear Algebra Appl. 18 (1977) 95-138.
12. J.B. Kruskal, Rank, decomposition, and uniqueness for 3-way and N-way arrays, in: R. Coppi, S. Bolasco (Eds.), Multiway Data Analysis, Elsevier, Amsterdam, 1989, pp. 7-18.
13. R. Bro, Comment to this paper in the INCTNC96 conference, 1996.
14. C.L. Lawson, R.J. Hanson, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ, 1974.
15. G. Dahlqvist, Å. Björk, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974.
16. J.B. Kruskal, R.A. Harshman, M.E. Lundy, How 3-MFA data can cause degenerate parafac solutions, among other relationships, in: R. Coppi, S. Bolasco (Eds.), Multiway Data Analysis, Elsevier, Amsterdam, 1989, pp. 115-130.
17. R.A. Harshman, M.E. Lundy, Private communication, 1996.
18. P.K. Hopke, P. Paatero, H. Jia, R.T. Ross, R.A. Harshman, A comparative review of four different PARAFAC programs, Chemometrics Intell. Lab. Syst. (1997), in preparation.