Factor analysis of hyphenated chromatographic data exploration, resolution and quantification of multicomponent systems.

Factor analysis (FA) is a family of widely used methods to obtain the underlying sources of variation of data tables. Typically, hyphenated chromatographic data provide data tables with one elution direction and another linked to the detector response. In this context, the factors are the eluting compounds and the profiles defining each factor are the elution profile and the pure response of the compound. This article describes the use of FA in chromatography through diverse tools and problems. Examples of determination of number of compounds, peak purity problems, resolution of overlapped compounds or extension to simultaneous analysis of multiple runs (higher-order data structures) to obtain qualitative and quantitative information are reviewed.

[1]  Helena Idborg,et al.  Multivariate approaches for efficient detection of potential metabolites from liquid chromatography/mass spectrometry data. , 2004, Rapid communications in mass spectrometry : RCM.

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

[3]  Romà Tauler,et al.  Determination of traces of herbicide mixtures in water by on-line solid-phase extraction followed by liquid chromatography with diode-array detection and multivariate self-modelling curve resolution , 1995 .

[4]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[5]  Edmund R. Malinowski,et al.  Investigation of window factor analysis and matrix regression analysis in chromatography , 1993 .

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

[7]  H. R. Keller,et al.  Artefacts in evolving factor analysis-based methods for peak purity control in liquid chromatography with diode-array detection , 1992 .

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

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

[10]  Dwight R Stoll,et al.  Analysis of four-way two-dimensional liquid chromatography-diode array data: application to metabolomics. , 2006, Analytical chemistry.

[11]  Romà Tauler,et al.  Multivariate Resolution of Coeluted Peaks in Hyphenated Liquid Chromatography ± Linear Sweep Voltammetry , 2003 .

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

[13]  Desire L. Massart,et al.  Multivariate peak purity approaches , 1996 .

[14]  Marcel Maeder,et al.  Evolving factor analysis, a new multivariate technique in chromatography , 1988 .

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

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

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

[18]  Efficiency of An Automatic Peak Purity Control Procedure in High-performance Liquid-chromatography Photodiode-array Coupling Based On Evolving Factor-analysis , 1993 .

[19]  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.

[20]  Luis A. Sarabia,et al.  Building robust calibration models for the analysis of estrogens by gas chromatography with mass spectrometry detection , 2004 .

[21]  Romà Tauler,et al.  Alternative calibration approaches for LC-MS quantitative determination of coeluted compounds in complex environmental mixtures using multivariate curve resolution. , 2007, Analytica chimica acta.

[22]  H. R. Keller,et al.  Heuristic evolving latent projections: resolving two-way multicomponent data. 2. Detection and resolution of minor constituents , 1992 .

[23]  R. Brereton,et al.  Influence of predicted elution regions on the performance of methods for evolutionary factor analysis as applied to high-performance liquid chromatography , 1995 .

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

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

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

[27]  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 .

[28]  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 .

[29]  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 .

[30]  Qing-Song Xu,et al.  Local resolution of hyphenated chromatographic data , 1999 .

[31]  P. Gemperline Practical Guide To Chemometrics , 2006 .

[32]  K. Markides,et al.  Chromatographic alignment by warping and dynamic programming as a pre-processing tool for PARAFAC modelling of liquid chromatography-mass spectrometry data. , 2002, Journal of chromatography. A.

[33]  R. Synovec,et al.  Objective data alignment and chemometric analysis of comprehensive two-dimensional separations with run-to-run peak shifting on both dimensions. , 2001, Analytical chemistry.

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

[35]  Desire L. Massart,et al.  Effect of the scan time on methods based on evolving factor analysis in liquid chromatography , 1992 .

[36]  Yizeng Liang,et al.  Determination of volatile components in ginger using gas chromatography-mass spectrometry with resolution improved by data processing techniques. , 2004, Journal of agricultural and food chemistry.

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

[38]  R. Brereton,et al.  Resolution of LC/1H NMR data applied to a three‐component mixture of polyaromatic hydrocarbons , 2002 .

[39]  Enric Comas,et al.  Quantification from highly drifted and overlapped chromatographic peaks using second-order calibration methods. , 2004, Journal of chromatography. A.

[40]  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.

[41]  Richard G. Brereton,et al.  Evaluation of parallel factor analysis for the resolution of kinetic data by diode-array high-performance liquid chromatography , 1997 .

[42]  Edmund R. Malinowski,et al.  Preferred set selection by iterative key set factor analysis , 1989 .

[43]  M. Jalali-Heravi,et al.  Characterization and determination of fatty acids in fish oil using gas chromatography-mass spectrometry coupled with chemometric resolution techniques. , 2004, Journal of chromatography. A.

[44]  P. Rose,et al.  Determination of Ultratrace-Level Fluorescent Tracer Concentrations in Environmental Samples Using a Combination of HPLC Separation and Laser-Excited Fluorescence Multiwavelength Emission Detection: Application to Testing of Geothermal Well Brines , 2001 .

[45]  F. Rius,et al.  Time shift correction in second-order liquid chromatographic data with iterative target transformation factor analysis , 2002 .

[46]  Fang Zhang,et al.  Resolution of multicomponent overlapped peaks A comparison of several curve resolution methods. , 2006, Talanta.

[47]  Luis A. Sarabia,et al.  Three-way models and detection capability of a gas chromatography–mass spectrometry method for the determination of clenbuterol in several biological matrices: the 2002/657/EC European Decision , 2004 .

[48]  D. Massart,et al.  Resolution of Complex Liquid Chromatography−Fourier Transform Infrared Spectroscopy Data , 1997 .

[49]  Romà Tauler,et al.  Validation of alternating least-squares multivariate curve resolution for chromatographic resolution and quantitation , 1996 .

[50]  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..

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

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

[53]  Bruce R. Kowalski,et al.  Generalized rank annihilation method , 1987 .

[54]  J. R. Torres-Lapasió,et al.  Resolution of multicomponent peaks by orthogonal projection approach, positive matrix factorization and alternating least squares , 2000 .

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

[56]  Brian K. Dable,et al.  Rapid multivariate curve resolution applied to near real-time process monitoring with HPLC/Raman data , 2005 .

[57]  Yizeng Liang,et al.  Comparative analysis of the volatile components in cut tobacco from different locations with gas chromatography-mass spectrometry (GC-MS) and combined chemometric methods. , 2006, Analytica chimica acta.

[58]  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 .

[59]  R. Tauler,et al.  Degradation study of benomyl and carbendazim in water by liquid chromatography and multivariate curve resolution methods , 1997 .

[60]  Richard G. Brereton,et al.  Determination of the Number of Significant Components in Liquid Chromatography Nuclear Magnetic Resonance Spectroscopy , 2004 .

[61]  B. W. Wright,et al.  A comprehensive two-dimensional retention time alignment algorithm to enhance chemometric analysis of comprehensive two-dimensional separation data. , 2005, Analytical chemistry.

[62]  Desire L. Massart,et al.  Resolution of multicomponent overlapped peaks by the orthogonal projection approach, evolving factor analysis and window factor analysis , 1997 .

[63]  Andrew G. Glen,et al.  APPL , 2001 .

[64]  Determination of phenolic acids in strawberry samples by means of fast liquid chromatography and multivariate curve resolution methods. , 2007, Talanta.

[65]  B. Lendl,et al.  High-performance liquid chromatography with diamond ATR–FTIR detection for the determination of carbohydrates, alcohols and organic acids in red wine , 2003, Analytical and bioanalytical chemistry.

[66]  Sarah C. Rutan,et al.  Analysis of three- and four-way data using multivariate curve resolution-alternating least squares with global multi-way kinetic fitting , 2006 .

[67]  A. de Juan,et al.  Three‐way data analysis of pollutant degradation profiles monitored using liquid chromatography–diode array detection , 1999 .

[68]  Romà Tauler,et al.  Application of multivariate self-modeling curve resolution to the quantitation of trace levels of organophosphorus pesticides in natural waters from interlaboratory studies , 1996 .

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

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

[71]  Romà Tauler,et al.  Assessment of new constraints applied to the alternating least squares method , 1997 .

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

[73]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[74]  Romà Tauler,et al.  Comparison of three‐way resolution methods for non‐trilinear chemical data sets , 2001 .

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

[76]  R. Bro PARAFAC. Tutorial and applications , 1997 .

[77]  Richard G Brereton,et al.  Application of multivariate curve resolution methods to on-flow LC-NMR. , 2005, Journal of chromatography. A.

[78]  Application of several modified peak purity assays to real complex multicomponent mixtures by high-performance liquid chromatography with diode-array detection. , 1999, Journal of chromatography. A.

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

[80]  Bruce R. Kowalski,et al.  Standardization of Second-Order Chromatographic/Spectroscopic Data for Optimum Chemical Analysis , 1998 .

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

[82]  Claus A. Andersson,et al.  PARAFAC2—Part II. Modeling chromatographic data with retention time shifts , 1999 .

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

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

[85]  Richard G. Brereton,et al.  Hard Modeling Methods for the Curve Resolution of Data from Liquid Chromatography with a Diode Array Detector and On-Flow Liquid Chromatography with Nuclear Magnetic Resonance Spectroscopy , 2006, J. Chem. Inf. Model..

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

[87]  Johan Lindberg,et al.  Predictive metabolite profiling applying hierarchical multivariate curve resolution to GC-MS data--a potential tool for multi-parametric diagnosis. , 2006, Journal of proteome research.

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

[89]  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 .

[90]  P.M.J. Coenegracht,et al.  Comparison of several curve resolution methods for drug impurity profiling using high-performance liquid chromatography with diode array detection , 2003 .

[91]  R. Tauler,et al.  Resolution and quantitative determination of coeluted pesticide mixtures in liquid chromatography–thermospray mass spectrometry by multivariate curve resolution , 1998 .

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

[93]  Window evolving factor analysis for assessment of peak homogeneity in liquid chromatography , 1993 .

[94]  B. Kowalski,et al.  Selectivity, local rank, three‐way data analysis and ambiguity in multivariate curve resolution , 1995 .

[95]  Alejandro C Olivieri,et al.  Interference-free analysis using three-way fluorescence data and the parallel factor model. Determination of fluoroquinolone antibiotics in human serum. , 2003, Analytical chemistry.

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

[97]  R. Bro,et al.  PARAFAC2—Part I. A direct fitting algorithm for the PARAFAC2 model , 1999 .

[98]  Desire L. Massart,et al.  Application of SIMPLISMA for the assessment of peak purity in liquid chromatography with diode array detection , 1994 .

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

[100]  Ina Schuppe-Koistinen,et al.  Screening of biomarkers in rat urine using LC/electrospray ionization-MS and two-way data analysis. , 2003, Analytical chemistry.

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

[102]  Romà Tauler,et al.  Multivariate Curve Resolution (MCR) from 2000: Progress in Concepts and Applications , 2006 .

[103]  Jamin C. Hoggard,et al.  Comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry analysis of metabolites in fermenting and respiring yeast cells. , 2006, Analytical chemistry.

[104]  Bruce R. Kowalski,et al.  Generalized rank annihilation method : II. Analysis of bimodal chromatographic data , 1987 .

[105]  F. Rius,et al.  Second-order bilinear calibration for determining polycyclic aromatic compounds in marine sediments by solvent extraction and liquid chromatography with diode-array detection , 2003 .

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

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

[108]  Ingvar Eide,et al.  Toxicological evaluation of complex mixtures: fingerprinting and multivariate analysis. , 2004, Environmental toxicology and pharmacology.

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

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

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

[112]  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 .

[113]  Edmund R. Malinowski,et al.  Factor Analysis in Chemistry , 1980 .

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

[115]  M. Jalali-Heravi,et al.  Use of second-order calibration for residue screening of some triazines in the presence of coeluting interferences by gas chromatography–selected ion mass spectrometry , 2005 .

[116]  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 .

[117]  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 .