Multivariate Curve Resolution (MCR) from 2000: Progress in Concepts and Applications

This work is mainly oriented to give an overview of the progress of multivariate curve resolution methods in the last 5 years. Conceived as a review that combines theory and practice, it will present the basics needed to understand what is the use, prospects and limitations of this family of chemometric methods with the latest trends in theoretical contributions and in the field of analytical applications.

[1]  P. Hopke,et al.  Analysis of ambient particle size distributions using Unmix and positive matrix factorization. , 2004, Environmental science & technology.

[2]  R. Tauler.  Multivariate curve resolution applied to second order data , 1995 .

[3]  G J de Jong,et al.  Optimisation of high-performance liquid chromatography with diode array detection using an automatic peak tracking procedure based on augmented iterative target transformation factor analysis. , 2004, The Analyst.

[4]  R. Tauler,et al.  Combining hard- and soft-modelling to solve kinetic problems , 2000 .

[5]  Yi-Zeng Liang,et al.  Principles and methodologies in self-modeling curve resolution , 2004 .

[6]  Julian Morris,et al.  Curve resolution for multivariate images with applications to TOF-SIMS and Raman , 2004 .

[7]  Anna de Juan,et al.  Soft Modeling of Analytical Data , 2006 .

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

[9]  Margaret Werner-Washburne,et al.  Hyperspectral microarray scanning: impact on the accuracy and reliability of gene expression data , 2005, BMC Genomics.

[10]  E. A. Sylvestre,et al.  Curve Resolution Using a Postulated Chemical Reaction , 1974 .

[11]  M. Esteban,et al.  Chemometrics for the analysis of voltammetric data , 2006 .

[12]  Jan van der Greef,et al.  Symbiosis of chemometrics and metabolomics: past, present, and future , 2005 .

[13]  Rasmus Bro,et al.  Multi-way Analysis with Applications in the Chemical Sciences , 2004 .

[14]  R. Bro,et al.  A fast non‐negativity‐constrained least squares algorithm , 1997 .

[15]  Philip K. Hopke,et al.  Incorporation of parametric factors into multilinear receptor model studies of Atlanta aerosol , 2003 .

[16]  D. L. Massart,et al.  Purity assessment and resolution of tetracycline hydrochloride samples analysed using high-performance liquid chromatography with diode array detection , 1999 .

[17]  A. Smilde,et al.  Fusion of mass spectrometry-based metabolomics data. , 2005, Analytical chemistry.

[18]  Alejandro C Olivieri,et al.  New method for the determination of benzoic and sorbic acids in commercial orange juices based on second-order spectrophotometric data generated by a pH gradient flow injection technique. , 2004, Journal of agricultural and food chemistry.

[19]  Romà Tauler,et al.  Exploratory data analysis of DNA microarrays by multivariate curve resolution. , 2006, Analytical biochemistry.

[20]  Romà Tauler,et al.  Resolution of a structural competition involving dimeric G-quadruplex and its C-rich complementary strand , 2006, Nucleic acids research.

[21]  Paul J. Gemperline,et al.  Characterizing batch reactions with in situ spectroscopic measurements, calorimetry and dynamic modeling , 2003 .

[22]  Peter D. Wentzell,et al.  A modification to window target-testing factor analysis using a Gaussian window , 2000 .

[23]  M. V. Van Benthem,et al.  Application of equality constraints on variables during alternating least squares procedures , 2002 .

[24]  Yann Batonneau,et al.  Combined use of conventional and second-derivative data in the SIMPLISMA self-modeling mixture analysis approach. , 2002, Analytical chemistry.

[25]  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..

[26]  Yi-Zeng Liang,et al.  Comparing chemical fingerprints of herbal medicines using modified window target-testing factor analysis , 2005, Analytical and bioanalytical chemistry.

[27]  Romà Tauler,et al.  On rotational ambiguity in model‐free analyses of multivariate data , 2006 .

[28]  Marcel Maeder,et al.  Target transform fitting: a new method for the non‐linear fitting of multivariate data with separable parameters , 2001 .

[29]  Romà Tauler,et al.  Chemometric modeling of main contamination sources in surface waters of Portugal , 2004, Environmental toxicology and chemistry.

[30]  Nicolaas (Klaas) M. Faber,et al.  Comment on a recently proposed resampling method , 2001 .

[31]  José Manuel Amigo,et al.  A mixed hard- and soft-modelling approach for the quantitative determination of oxipurines and uric acid in human urine , 2006 .

[32]  Bogusława Czarnik-Matusewicz,et al.  Temperature-dependent water structural transitions examined by near-IR and mid-IR spectra analyzed by multivariate curve resolution and two-dimensional correlation spectroscopy , 2005 .

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

[34]  Sarah C. Rutan,et al.  Steady state kinetic model constraint for Multivariate Curve Resolution-Alternating Least Squares analysis , 2005 .

[35]  Róbert Rajkó,et al.  Analytical solution for determining feasible regions of self‐modeling curve resolution (SMCR) method based on computational geometry , 2005 .

[36]  Riccardo Leardi,et al.  Three‐mode principal component analysis of monitoring data from Venice lagoon , 2000 .

[37]  Romà Tauler,et al.  Chemometrics applied to unravel multicomponent processes and mixtures: Revisiting latest trends in multivariate resolution , 2003 .

[38]  Cyril Ruckebusch,et al.  Multivariate Curve Resolution Methods in Imaging Spectroscopy: Influence of Extraction Methods and Instrumental Perturbations , 2003, J. Chem. Inf. Comput. Sci..

[39]  Sally S. Hunnicutt,et al.  Study of Complexation in Methanol/Water Mixtures by Infrared and Raman Spectroscopy and Multivariate Curve Resolution—Alternating Least-Squares Analysis , 2003, Applied spectroscopy.

[40]  Yi-Zeng Liang,et al.  On simplex-based method for self-modeling curve resolution of two-way data , 2003 .

[41]  R. Henry.  Multivariate receptor modeling by N-dimensional edge detection , 2003 .

[42]  N. Sidiropoulos,et al.  Least squares algorithms under unimodality and non‐negativity constraints , 1998 .

[43]  Romà Tauler,et al.  A graphical user-friendly interface for MCR-ALS: a new tool for multivariate curve resolution in MATLAB , 2005 .

[44]  E. Karjalainen.  The spectrum reconstruction problem: use of alternating regression for unexpected spectral components in two-dimensional spectroscopies , 1989 .

[45]  F. X. Rius,et al.  Multivariate resolution of rank-deficient near-infrared spectroscopy data from the reaction of curing epoxy resins using the rank augmentation strategy and multivariate curve resolution alternating least squares approach , 2004 .

[46]  Olav M. Kvalheim,et al.  Eigenstructure tracking analysis for revealing noise pattern and local rank in instrumental profiles: application to transmittance and absorbance IR spectroscopy , 1993 .

[47]  Rasmus Bro,et al.  Comparison of PARAFAC2 and MCR-ALS for resolution of an analytical liquid dilution system , 2006 .

[48]  D. Massart,et al.  Orthogonal projection approach applied to peak purity assessment. , 1996, Analytical chemistry.

[49]  M P Callao,et al.  Sequential injection analysis for the simultaneous determination of clavulanic acid and amoxicillin in pharmaceuticals using second-order calibration. , 2006, Analytical sciences : the international journal of the Japan Society for Analytical Chemistry.

[50]  R. Tauler,et al.  Estimation of figures of merit using univariate statistics for quantitative second-order multivariate curve resolution , 2001 .

[51]  P. Paatero.  The Multilinear Engine—A Table-Driven, Least Squares Program for Solving Multilinear Problems, Including the n-Way Parallel Factor Analysis Model , 1999 .

[52]  P. Wentzell,et al.  Dynamic Monte Carlo self-modeling curve resolution method for multicomponent mixtures , 2002 .

[53]  Richard G Brereton,et al.  Combined kinetics and iterative target transformation factor analysis for spectroscopic monitoring of reactions. , 2006, The Analyst.

[54]  Age K. Smilde,et al.  Estimating reaction rate constants from a two‐step reaction: a comparison between two‐way and three‐way methods , 2000 .

[55]  P. Gemperline,et al.  Computation of the range of feasible solutions in self-modeling curve resolution algorithms. , 1999, Analytical chemistry.

[56]  J. Mesirov,et al.  Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. , 1999, Science.

[57]  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 .

[58]  R. Manne,et al.  Use of convexity for finding pure variables in two-way data from mixtures , 2000 .

[59]  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 .

[60]  Cyril Ruckebusch,et al.  Multivariate curve resolution of step-scan FTIR spectral data , 2004 .

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

[62]  R. Tauler,et al.  Implementation of a chemical equilibrium constraint in the multivariate curve resolution of voltammograms from systems with successive metal complexes. , 2001, The Analyst.

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

[64]  P. Paatero,et al.  Positive matrix factorization applied to a curve resolution problem , 1998 .

[65]  Age K Smilde,et al.  Near-Infrared Spectroscopic Monitoring of a Series of Industrial Batch Processes Using a Bilinear Grey Model , 2003, Applied spectroscopy.

[66]  Marcel Maeder,et al.  Exhaustive evolving factor analysis (E‐EFA) , 2001 .

[67]  Nathalie Dupuy,et al.  Reliability of the contribution profiles obtained through the SIMPLISMA approach and used as reference in a calibration process: Application to Raman micro-analysis of dust particles , 2003 .

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

[69]  Qing-Song Xu,et al.  Alternative moving window factor analysis for comparison analysis between complex chromatographic data. , 2006, Journal of chromatography. A.

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

[71]  Romà Tauler,et al.  Comparison of different multiway methods for the analysis of geographical metal distributions in fish, sediments and river waters in Catalonia , 2007 .

[72]  Romà Tauler,et al.  Multivariate extension of the continuous variation and mole-ratio methods for the study of the interaction of intercalators with polynucleotides , 2000 .

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

[74]  Philip K. Hopke,et al.  Estimation of the heteroscedastic noise in large data arrays , 2000 .

[75]  Romà Tauler,et al.  Multivariate curve resolution applied to the analysis and resolution of two-dimensional [1H,15N] NMR reaction spectra. , 2004, Analytical chemistry.

[76]  Romà Tauler,et al.  Local rank exploratory analysis of evolving rank-deficient systems , 2004 .

[77]  Desire L. Massart,et al.  Multiple factor analysis in environmental chemistry , 2005 .

[78]  M. Maeder,et al.  Nonlinear least-squares fitting of multivariate absorption data , 1990 .

[79]  Paul J. Gemperline,et al.  Non‐negativity constraints for elimination of multiple solutions in fitting of multivariate kinetic models to spectroscopic data , 2005 .

[80]  Romà Tauler,et al.  Quality assessment of the results obtained by multivariate curve resolution analysis of multiple runs of gasoline blending processes , 2006 .

[81]  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 .

[82]  Romà Tauler,et al.  Application of chemometric methods to the investigation of main microcontaminant sources of endocrine disruptors in coastal and harbour waters and sediments , 2004, Analytical and bioanalytical chemistry.

[83]  F. X. Rius,et al.  Development and validation of a method for determining pesticides in groundwater from complex overlapped HPLC signals and multivariate curve resolution , 2005 .

[84]  Edmund R. Malinowski,et al.  Automatic window factor analysis—A more efficient method for determining concentration profiles from evolutionary spectra , 1996 .

[85]  Rasmus Bro,et al.  Multi-way analysis for investigation of industrial pectin using an analytical liquid dilution system , 2006 .

[86]  Romà Tauler,et al.  Calculation of band boundaries of feasible solutions obtained by Multivariate Curve Resolution–Alternating Least Squares of multiple runs of a reaction monitored by NIR spectroscopy , 2005 .

[87]  Romà Tauler,et al.  Fast chromatography of complex biocide mixtures using diode array detection and multivariate curve resolution , 2004 .

[88]  Barry M. Wise,et al.  A new approach for interactive self-modeling mixture analysis , 2005 .

[89]  Romà Tauler,et al.  Analysis of environmental samples by application of multivariate curve resolution on fused high-performance liquid chromatography-diode array detection mass spectrometry data. , 2006, Journal of chromatography. A.

[90]  Romà Tauler,et al.  Voltammetry assisted by multivariate analysis as a tool for speciation of metallothioneins: Competitive complexation of α- and β-metallothionein domains with cadmium and zinc , 2003 .

[91]  P. Gemperline,et al.  Advantages of soft versus hard constraints in self-modeling curve resolution problems. Alternating least squares with penalty functions. , 2003, Analytical chemistry.

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

[93]  Miquel Esteban,et al.  Multivariate Curve Resolution of Cyclic Voltammetric Data: Application to the Study of the Cadmium-Binding Properties of Glutathione , 1999 .

[94]  Yi-Zeng Liang,et al.  Sectional moving window factor analysis for diagnosing elution chromatographic patterns , 2003 .

[95]  Ji-Hong Wang,et al.  Discriminant image resolution: a novel multivariate image analysis method utilizing a spatial classification constraint in addition to bilinear nonnegativity , 2005 .

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

[97]  R. Tauler,et al.  Chapter 16 Interpretation of environmental data using chemometrics , 2000 .

[98]  M. Maeder,et al.  The resolution of overlapping chromatographic peaks by evolving factor analysis , 1986 .

[99]  Romà Tauler,et al.  Local rank analysis for exploratory spectroscopic image analysis. Fixed Size Image Window-Evolving Factor Analysis , 2005 .

[100]  Javier Saurina,et al.  Quantitative determinations in conventional flow injection analysis based on different chemometric calibration statregies: a review , 2001 .

[101]  Jordi Mas,et al.  Elucidating the composition profiles of alcoholic fermentations by use of ALS methodology , 2005 .

[102]  R. Manne,et al.  Resolution of two-way data from hyphenated chromatography by means of elementary matrix transformations , 2000 .

[103]  José Manuel Amigo,et al.  A mixed hard- and soft-modelling approach to study and monitor enzymatic systems in biological fluids , 2006 .

[104]  P. Hopke.  Receptor modeling in environmental chemistry , 1985 .

[105]  Yann Batonneau,et al.  Speciation of PM10 sources of airborne nonferrous metals within the 3-km zone of lead/zinc smelters. , 2004, Environmental science & technology.

[106]  Sarah C. Rutan,et al.  Multivariate curve resolution with non-linear fitting of kinetic profiles , 2001 .

[107]  Philip K. Hopke,et al.  Utilizing wind direction and wind speed as independent variables in multilinear receptor modeling studies , 2002 .

[108]  Romà Tauler,et al.  Detection and resolution of intermediate species in protein folding processes using fluorescence and circular dichroism spectroscopies and multivariate curve resolution. , 2002, Analytical chemistry.

[109]  J. C. Merlin,et al.  Polarization Effects of Confocal Raman Microspectrometry of Crystal Powders Using Interactive Self-Modeling Analysis , 2003 .

[110]  Desire L. Massart,et al.  Application of the needle algorithm for exploratory analysis and resolution of HPLC-DAD data , 1996 .

[111]  Romà Tauler,et al.  Application of a combination of hard and soft modeling for equilibrium systems to the quantitative analysis of pH-modulated mixture samples. , 2003, Analytical chemistry.

[112]  Yukihiro Ozaki,et al.  Resolution of two‐way data from spectroscopic monitoring of reaction or process systems by parallel vector analysis (PVA) and window factor analysis (WFA): inspection of the effect of mass balance, methods and simulations , 2003 .

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

[114]  Romà Tauler,et al.  Modeling temperature-dependent protein structural transitions by combined near-IR and mid-IR spectroscopies and multivariate curve resolution. , 2003, Analytical chemistry.

[115]  Romà Tauler,et al.  Spectroscopic imaging and chemometrics: a powerful combination for global and local sample analysis , 2004 .

[116]  R. Tauler.  Calculation of maximum and minimum band boundaries of feasible solutions for species profiles obtained by multivariate curve resolution , 2001 .

[117]  Romà Tauler,et al.  Strategies for solving matrix effects in the analysis of triphenyltin in sea-water samples by three-way multivariate curve resolution , 2000 .

[118]  Age K. Smilde,et al.  Sufficient conditions for unique solutions within a certain class of curve resolution models , 2001 .

[119]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[120]  Yi-Zeng Liang,et al.  Recursive evolving spectral projection for revealing the concentration windows of overlapping peaks in two-way chromatographic experiments , 2004 .

[121]  Philip K. Hopke,et al.  Recent developments in receptor modeling , 2003 .

[122]  Yi-Zeng Liang,et al.  Resolution of the Embedded Chromatographic Peaks by Modified Orthogonal Projection Resolution and Entropy Maximization Method , 2000 .

[123]  F. Xavier Rius,et al.  Influence of selectivity and sensitivity parameters on detection limits in multivariate curve resolution of chromatographic second-order data , 2003 .

[124]  R. Tauler,et al.  Identification and distribution of contamination sources in the Ebro river basin by chemometrics modelling coupled to geographical information systems. , 2006, Talanta.

[125]  H. Gampp,et al.  Calculation of equilibrium constants from multiwavelength spectroscopic data-IV Model-free least-squares refinement by use of evolving factor analysis. , 1986, Talanta.

[126]  Romà Tauler,et al.  Solving liquid chromatography mass spectrometry coelution problems in the analysis of environmental samples by multivariate curve resolution. , 2005, Journal of chromatography. A.

[127]  Rasmus Bro,et al.  Jack-knife technique for outlier detection and estimation of standard errors in PARAFAC models , 2003 .

[128]  Y Liang,et al.  Resolution of two-way data: theoretical background and practical problem-solving Part 1: Theoretical background and methodology , 2001, Fresenius' journal of analytical chemistry.

[129]  P. Hopke,et al.  Application of modified alternating least squares regression to spectroscopic image analysis , 2003 .

[130]  Romà Tauler,et al.  Multivariate curve resolution applied to three‐way trilinear data: Study of a spectrofluorimetric acid–base titration of salicylic acid at three excitation wavelengths , 1998 .

[131]  Age K. Smilde,et al.  Application of curve resolution based methods to kinetic data , 1999 .

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

[133]  Johan Trygg,et al.  High-throughput data analysis for detecting and identifying differences between samples in GC/MS-based metabolomic analyses. , 2005, Analytical chemistry.

[134]  Graeme Puxty,et al.  Tutorial on the fitting of kinetics models to multivariate spectroscopic measurements with non-linear least-squares regression , 2006 .

[135]  R. Tauler,et al.  Noise propagation and error estimations in multivariate curve resolution alternating least squares using resampling methods , 2004 .

[136]  R. Manne.  On the resolution problem in hyphenated chromatography , 1995 .

[137]  Yi-Zeng Liang,et al.  Subwindow factor analysis , 1999 .

[138]  R Huo,et al.  Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting. , 2004, Journal of magnetic resonance.

[139]  Romà Tauler,et al.  Principal component analysis applied to the study of successive complex formation data in Cu(II)–ethanolamine systems , 2005 .

[140]  M. Maeder,et al.  Resolving factor analysis. , 2001, Analytical chemistry.

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

[142]  Edmund R. Malinowski,et al.  Obtaining the key set of typical vectors by factor analysis and subsequent isolation of component spectra , 1982 .