Selectivity, local rank, three‐way data analysis and ambiguity in multivariate curve resolution

A new multivariate curve resolution method is presented and tested with data of various levels of complexity. Rotational and intensity ambiguities and the effect of selectivity on resolution are the focus. Analysis of simulated data provides the general guidelines concerning the conditions for uniqueness of a solution for a given problem. Multivariate curve resolution is extended to the analysis of three‐way data matrices. The particular case of three‐way data where only one of the orders is common between slices is studied in some detail.

[1]  E. A. Sylvestre,et al.  Self Modeling Curve Resolution , 1971 .

[2]  D. J. Leggett,et al.  Numerical analysis of multicomponent spectra , 1977 .

[3]  Edmund R. Malinowski,et al.  Determination of the number of factors and the experimental error in a data matrix , 1977 .

[4]  S. Wold Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

[5]  Harald Martens,et al.  Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures , 1982 .

[6]  Paul J. Gemperline,et al.  A priori estimates of the elution profiles of the pure components in overlapped liquid chromatography peaks using target factor analysis , 1984, J. Chem. Inf. Comput. Sci..

[7]  H. Gampp,et al.  Calculation of equilibrium constants from multiwavelength spectroscopic data-III Model-free analysis of spectrophotometric and ESR titrations. , 1985, Talanta.

[8]  Bruce R. Kowalski,et al.  An extension of the multivariate component-resolution method to three components , 1985 .

[9]  G. Kateman,et al.  Multicomponent self-modelling curve resolution in high-performance liquid chromatography by iterative target transformation analysis , 1985 .

[10]  Bruce R. Kowalski,et al.  Generalized rank annihilation factor analysis , 1986 .

[11]  Odd S. Borgen,et al.  The multivariate N-Component resolution problem with minimum assumptions , 1986 .

[12]  Gerrit Kateman,et al.  Evaluation of curve resolution and iterative target transformation factor analysis in quantitative analysis by liquid chromatography , 1987 .

[13]  H. Gampp,et al.  Quantification of a known component in an unknown mixture , 1987 .

[14]  S. Wold,et al.  Local principal component models, rank maps and contextuality for curve resolution and multi-way calibration inference , 1987 .

[15]  M. Maeder Evolving factor analysis for the resolution of overlapping chromatographic peaks , 1987 .

[16]  Bruce R. Kowalski,et al.  Tensorial calibration: I. First‐order calibration , 1988 .

[17]  Enric Casassas,et al.  Application of principal component analysis to the study of multiple equilibria systems : Study of copper(II)/salicylate/mono-, di- and triethanolamine systems , 1989 .

[18]  J. Hamilton,et al.  Mixture analysis using factor analysis. II: Self‐modeling curve resolution , 1990 .

[19]  B. Kowalski,et al.  Tensorial resolution: A direct trilinear decomposition , 1990 .

[20]  W. Windig,et al.  Interactive self-modeling mixture analysis , 1991 .

[21]  H. R. Keller,et al.  Peak purity control in liquid chromatography with photodiode-array detection by a fixed size moving window evolving factor analysis , 1991 .

[22]  Romà Tauler,et al.  Self-modelling curve resolution in studies of spectrometric titrations of multi-equilibria systems by factor analysis , 1991 .

[23]  Age K. Smilde,et al.  Three‐way methods for the calibration of chromatographic systems: Comparing PARAFAC and three‐way PLS , 1991 .

[24]  W. Windig Self-modeling mixture analysis of spectral data with continuous concentration profiles , 1992 .

[25]  R. Tauler,et al.  Deconvolution and quantitation of unresolved mixtures in liquid chromatographic-diode array detection using evolving factor analysis , 1992 .

[26]  W. Windig,et al.  Self-modeling mixture analysis of second-derivative near-infrared spectral data using the SIMPLISMA approach , 1992 .

[27]  Edmund R. Malinowski,et al.  Window factor analysis: Theoretical derivation and application to flow injection analysis data , 1992 .

[28]  H. R. Keller,et al.  Evolving factor analysis in the presence of heteroscedastic noise , 1992 .

[29]  E. Karjalainen,et al.  Simultaneous analysis of multiple chromatographic runs and samples with alternating regression , 1992 .

[30]  Yizeng Liang,et al.  Heuristic evolving latent projections: resolving two-way multicomponent data. 1. Selectivity, latent-projective graph, datascope, local rank, and unique resolution , 1992 .

[31]  R. Tauler,et al.  Spectroscopic resolution of macromolecular complexes using factor analysis: Cu(II) -polyethyleneimine system , 1992 .

[32]  R. Tauler,et al.  Application of factor analysis to speciation in multiequilibria systems , 1992 .

[33]  B. Kowalski,et al.  Advances in second‐order calibration , 1993 .

[34]  R. Tauler,et al.  Multivariate curve resolution applied to liquid chromatography—diode array detection , 1993 .

[35]  B. Kowalski,et al.  Multivariate curve resolution applied to spectral data from multiple runs of an industrial process , 1993 .

[36]  Romà Tauler,et al.  Simultaneous analysis of several spectroscopic titrations with self-modelling curve resolution , 1993 .

[37]  Romà Tauler,et al.  Interactions of H+ and Cu(II) Ions with Poly(adenylic acid): Study by Factor Analysis , 1994 .

[38]  B. Kowalski,et al.  Theory of medium‐rank second‐order calibration with restricted‐Tucker models , 1994 .