PARAFAC. Tutorial and applications

Harshman, 1970, Foundations of the PARAFAC procedure: Model and conditions for an ‘explanatory’ multi-mode factor analysis, UCLA Working Papers in phonetics, 16, 1

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

Geladi, 1989, Analysis of multi-way (multi-mode) data, Chemom. Intell. Lab. Syst., 7, 11, 10.1016/0169-7439(89)80108-X

Smilde, 1992, Three-way analyses. Problems and prospects, Chemom. Intell. Lab. Syst., 5, 143, 10.1016/0169-7439(92)85005-N

Kroonenburg, 1983, Three-mode principal component analysis

Kiers, 1991, Hierarchical relations among three-way methods, Psychometrika, 56, 449, 10.1007/BF02294485

Seasholz, 1993, The parsimony principle applied to multivariate calibration, Anal. Chim. Acta, 277, 165, 10.1016/0003-2670(93)80430-S

Harshman, 1981, Basic concepts underlying the PARAFAC-CANDECOMP three-way factor analysis model and its application to longitudinal data, 435

Burdick, 1995, An introduction to tensor products with applications to multiway data analysis, Chemom. Intell. Lab. Syst., 28, 229, 10.1016/0169-7439(95)98599-2

Scarminio, 1993, Analysis of correlated spectral data, Anal. Chem., 65, 409, 10.1021/ac00052a017

Sarabia, 1993, A program for non-orthogonal factor analysis, Trends Anal. Chem., 12, 226, 10.1016/0165-9936(93)87061-2

Faber, 1994, Generalized rank annihilation method I: derivation of eignevalue problems, J. Chemom., 8, 147, 10.1002/cem.1180080206

Harshman, 1972, Determination and proof of minimum uniqueness conditions for PARAFAC1, UCLA Working Papers in phonetics, 22, 111

Kruskal, 1976, More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling, Psychometrika, 41, 281, 10.1007/BF02293554

Kruskal, 1977, Three-way arrays: Rank and uniqueness of trilinear decomposition, with application to arithmetic complexity and statistics, Linear Algebra Appl., 18, 95, 10.1016/0024-3795(77)90069-6

Cattell, 1944, Parallel proportional profiles and other principles for determining the choice of factors by rotation, Psychometrika, 9, 267, 10.1007/BF02288739

Leurgans, 1993, A decomposition for three-way arrays, SIAM J. Matrix Anal. Appl., 14, 1064, 10.1137/0614071

Kruskal, 1989, Rank, decomposition, and uniqueness for 3-way and N-way arrays

Harshman, 1984, The PARAFAC model for three-way factor analysis and multidimensional scaling

ten Berge, 1988, Explicit Candecomp/PARAFAC solution for a contrived 2 × 2 × 2 array of rank three, Psychometrika, 53, 579, 10.1007/BF02294409

Ten Berge, 1991, Kruskal's polynomial for 2×2×2 arrays and a generalization to 2 ×n×n arrays, Psychometrika, 56, 631, 10.1007/BF02294495

Kiers, 1991, An efficient algorithm for PARAFAC of three-way data with large numbers of observation units, Psychometrika, 56, 147, 10.1007/BF02294592

Harshman, 1994, PARAFAC: Parallel factor analysis, Comp. Stat. Data Anal., 18, 39, 10.1016/0167-9473(94)90132-5

Sands, 1980, Component models for three-way data: An alternating least squares algorithm with optimal scaling features, Psychometrika, 45, 39, 10.1007/BF02293598

Burdick, 1990, Resolution of multicomponent fluorescent mixtures by analysis of excitation-emission-frequency array, J. Chemom., 4, 15, 10.1002/cem.1180040104

Sanchez, 1990, Tensorial resolution: A direct trilinear decomposition, J. Chemom., 4, 29, 10.1002/cem.1180040105

Li, 1993, Eliminating complex eigenvectors and eigenvalues in multiway analyses using the direct trilinear decomposition method, J. Chemom., 7, 77, 10.1002/cem.1180070202

Leurgans, 1992, Multilinear models in spectroscopy, Statist. Sci., 7, 289, 10.1214/ss/1177011225

Mitchell, 1993, An empirical comparison of resolution methods for three-way arrays, Chemom. Intell. Lab. Syst., 20, 149, 10.1016/0169-7439(93)80011-6

Tu, 1992, Resolution of trilinear mixtures: Application in spectroscopy, Stat. Sinica, 2, 577

Cliff, 1966, Orthogonal rotation to congruence, Psychometrika, 31, 33, 10.1007/BF02289455

Lawson, 1995, Solving least squares problems, 10.1137/1.9781611971217

Hanson, 1986, Linear least squares with bounds and linear constraints, SIAM J. Sci. Stat. Comput., 7, 826, 10.1137/0907055

Späth, 1987

Barlow, 1988, Error analysis and implementation aspects of deferred correction for equality constrained least squares problems, SIAM J. Numer. Anal., 25, 1340, 10.1137/0725076

Barlow, 1988, Iterative methods for equality-constrained least squares problems, SIAM J. Sci. Stat. Comput., 9, 892, 10.1137/0909061

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

Ross, 1995, Component resolution using multilinear models, Methods Enzymol., 246, 679, 10.1016/0076-6879(95)46029-2

ten Berge, 1989, Convergence of PARAFAC preprocessing procedures and the Deming-Stephan method of iterative proportional fitting

Kruskal, 1983, Multilinear methods, 28, 75

Harshman, 1984, Data preprocessing and the extended PARAFAC model

Cook, 1982

Smilde, 1992, Simple validatory tools for judging the predictive performance of PARAFAC and threeway PLS, J. Chemom., 6, 11, 10.1002/cem.1180060103

Durell, 1990, Factor analysis of the near-ultraviolet absorption spectrum of plastocyanin using bilinear, trilinear and quadrilinear models, Arch. Biochem. Biophys., 278, 148, 10.1016/0003-9861(90)90243-R

Mitchell, 1994, Slowly converging PARAFAC sequences: Swamps and two-fator degeneracies, J. Chemom., 8, 155, 10.1002/cem.1180080207

Krijnen, 1993, The analysis of three-way arrays by constrained PARAFAC methods

Kruskal, 1984, Multilinear methods

Kruskal, 1989, How 3-MFA data can cause degenerate PARAFAC solutions, among other relationships

Smilde, 1994, Theory of medium rank second-order calibration with restricted-Tucker models, J. Chemom., 21, 10.1002/cem.1180080104

Smilde, 1994, Multicomponent determination of chlorinated hydrocarbons using a reaction-based chemical sensor. 3. Medium-rank second-order calibration with restricted Tucker models, Anal. Chem., 66, 3345, 10.1021/ac00092a010

Harshman, 1972, PARAFAC2: Mathematical and technical notes, UCLA Working Papers in Phonetics, 22, 30

Kiers, 1993, An alternating least squares algorithm for PARAFAC2 and three-way DEDICOM, Comp. Stat. Data Anal., 16, 103, 10.1016/0167-9473(93)90247-Q

Kettenring, 1983, A case study in data analysis, 28, 105

Aastveit, 1984, ANOVA interactions by partial least squares regression, Biometrics, 42, 829, 10.2307/2530697

Martens, 1986, Partial least squares regression on design variables as an alternative to analysis of variance, Anal. Chim. Acta, 191, 133, 10.1016/S0003-2670(00)86303-5

Martinez, 1995, The biochemistry and control of enzymatic browning, Trends Food Sci. Technol., 6, 195, 10.1016/S0924-2244(00)89054-8

H. Heimdal, L.M. Larsen, L. Poll, R. Bro, Oxidation of chlorogenic acid and (-)-epicatiechin by letucce polyphenol oxidase in model solutions at various combinations of O2, CO2, Temperature and pH, J. Agric. Food Chem., in press.

Bro, 1996, Enzymatic browning of vegetables, 34, 85

N⊘orgaard, 1995, Classification and prediction of quality and process parameters of thick juice and beet sugar by fluorescence spectroscopy and chemometrics, Zuckerind., 120, 970

Ewing, 1985

N⊘orgaard, 1995, A multivariate chemometric approach to fluorescence spectroscopy, Talanta, 42, 1305, 10.1016/0039-9140(95)01586-Z

Bro, 1996, Multiway calibration, Multilinear PLS, J. Chemom., 10, 47, 10.1002/(SICI)1099-128X(199601)10:1<47::AID-CEM400>3.0.CO;2-C