Recent advances in analytical calibration with multi-way data

This critical review discusses the advances which have taken place in recent years in the field of multi-way instrumental data, i.e., data that can be arranged into a mathematical object of at least three ways (when they are measured for a group of samples). Particular focus is directed towards research works describing quantitative analytical calibrations. The development of data processing algorithms and the estimation of figures of merit are reviewed, along with the progress in the experimental generation of new three-, four- and five-way data of spectroscopic, chromatographic and electrochemical origin.

[1]  S. Wold,et al.  Residual bilinearization. Part 1: Theory and algorithms , 1990 .

[2]  A. J. Girón,et al.  Four-way calibration applied to the simultaneous determination of folic acid and methotrexate in urine samples , 2006 .

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

[4]  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.

[5]  Gabriela A Ibañez,et al.  Three-way partial least-squares/residual bilinearization study of second-order lanthanide-sensitized luminescence excitation-time decay data: analysis of benzoic acid in beverage samples. , 2008, Analytica chimica acta.

[6]  Patricia C Damiani,et al.  Four-way kinetic-excitation-emission fluorescence data processed by multi-way algorithms. Determination of carbaryl and 1-naphthol in water samples in the presence of fluorescent interferents. , 2010, Analytica chimica acta.

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

[8]  Graciela M. Escandar,et al.  Second-order and higher-order multivariate calibration methods applied to non-multilinear data using different algorithms , 2011 .

[9]  Rasmus Bro,et al.  Automated alignment of chromatographic data , 2006 .

[10]  G. M. Escandar,et al.  Flow injection analysis with on-line nylon powder extraction for room-temperature phosphorescence determination of thiabendazole. , 2009, Analytica chimica acta.

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

[12]  C. Fraga,et al.  The chemometric resolution and quantification of overlapped peaks form comprehensive two-dimensional liquid chromatography. , 2005, Journal of chromatography. A.

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

[14]  van der Linden,et al.  Definition and classification of interferences in analytical procedures , 1989 .

[15]  Alejandro C. Olivieri,et al.  Trilinear least-squares and unfolded-PLS coupled to residual trilinearization: New chemometric tools for the analysis of four-way instrumental data , 2006 .

[16]  Klaas Faber,et al.  New developments for the sensitivity estimation in four-way calibration with the quadrilinear parallel factor model. , 2012, Analytical chemistry.

[17]  Jamin C. Hoggard,et al.  Recent advancements in comprehensive two-dimensional separations with chemometrics. , 2008, Journal of chromatography. A.

[18]  Juan A Arancibia,et al.  Non-trilinear chromatographic time retention-fluorescence emission data coupled to chemometric algorithms for the simultaneous determination of 10 polycyclic aromatic hydrocarbons in the presence of interferences. , 2009, Analytical chemistry.

[19]  Alejandro García-Reiriz,et al.  Multiway partial least-squares coupled to residual trilinearization: a genuine multidimensional tool for the study of third-order data. Simultaneous analysis of procaine and its metabolite p-aminobenzoic acid in equine serum. , 2007, Analytical chemistry.

[20]  A. Muñoz de la Peña,et al.  Evaluation of unfolded-partial least-squares coupled to residual trilinearization for four-way calibration of folic acid and methotrexate in human serum samples. , 2007, Talanta.

[21]  R. Tauler,et al.  Multivariate curve resolution of overlapping voltammetric peaks: quantitative analysis of binary and quaternary metal mixtures. , 2002, The Analyst.

[22]  J. Kalivas,et al.  Selectivity and Related Measures for nth-Order Data. , 1996, Analytical chemistry.

[23]  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.

[24]  Age K Smilde,et al.  Quantitative analysis of target components by comprehensive two-dimensional gas chromatography. , 2003, Journal of chromatography. A.

[25]  U. Brinkman,et al.  Recent developments in the application of comprehensive two-dimensional gas chromatography. , 2008, Journal of chromatography. A.

[26]  R. Bro.  Review on Multiway Analysis in Chemistry—2000–2005 , 2006 .

[27]  A. Olivieri,et al.  A closed‐form expression for computing the sensitivity in second‐order bilinear calibration , 2005 .

[28]  S. Rutan,et al.  Chemometric Resolution and Quantification of Four-Way Data Arising from Comprehensive 2D-LC-DAD Analysis of Human Urine. , 2011, Chemometrics and intelligent laboratory systems : an international journal sponsored by the Chemometrics Society.

[29]  A. Lorber.  Error propagation and figures of merit for quantification by solving matrix equations , 1986 .

[30]  Pat Sandra,et al.  Comprehensive liquid chromatography: fundamental aspects and practical considerations--a review. , 2009, Analytica chimica acta.

[31]  Gabriela A Ibañez,et al.  Second-order analyte quantitation under identical profiles in one data dimension. A dependency-adapted partial least-squares/residual bilinearization method. , 2010, Analytical chemistry.

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

[33]  Hamid Abdollahi,et al.  Second-Order Data Obtained from Differential Pulse Voltammetry: Determination of Lead in River Water Using Multivariate Curve Resolution-Alternating Least-Squares (MCR-ALS) , 2010 .

[34]  Dwight R Stoll,et al.  Fast, comprehensive two-dimensional liquid chromatography. , 2007, Journal of chromatography. A.

[35]  A. Espinosa-Mansilla,et al.  Adsorptive stripping square wave voltammetry (Ad-SSWV) accomplished with second-order multivariate calibration determination of fenitrothion and its metabolites in river water samples. , 2008, Analytica chimica acta.

[36]  Yang Li,et al.  A novel trilinear decomposition algorithm for second-order linear calibration , 2000 .

[37]  Alejandro C Olivieri,et al.  Analytical advantages of multivariate data processing. One, two, three, infinity? , 2008, Analytical chemistry.

[38]  A. Olivieri.  On a versatile second‐order multivariate calibration method based on partial least‐squares and residual bilinearization: Second‐order advantage and precision properties , 2005 .

[39]  Rasmus Bro,et al.  Solving fundamental problems in chromatographic analysis , 2008, Analytical and bioanalytical chemistry.

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

[41]  R. Synovec,et al.  Trilinear chemometric analysis of two-dimensional comprehensive gas chromatography-time-of-flight mass spectrometry data. , 2004, Journal of chromatography. A.

[42]  R. Bro,et al.  Practical aspects of PARAFAC modeling of fluorescence excitation‐emission data , 2003 .

[43]  G. M. Escandar,et al.  Second-order multivariate calibration procedures applied to high-performance liquid chromatography coupled to fast-scanning fluorescence detection for the determination of fluoroquinolones. , 2009, Journal of chromatography. A.

[44]  Bruce R. Kowalski,et al.  Extension of Trilinear Decomposition Method with an Application to the Flow Probe Sensor , 1994 .

[45]  Santiago A. Bortolato,et al.  A novel application of nylon membranes to the luminescent determination of benzo[a]pyrene at ultra trace levels in water samples. , 2008, Analytica chimica acta.

[46]  Hai-Long Wu,et al.  A new third‐order calibration method with application for analysis of four‐way data arrays , 2011 .

[47]  Rolf Sundberg,et al.  Precision of prediction in second‐order calibration, with focus on bilinear regression methods , 2002 .

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

[49]  Miloslav Pravda,et al.  ROLE OF CHEMOMETRICS FOR ELECTROCHEMICAL SENSORS , 2002 .

[50]  Alejandro C. Olivieri,et al.  A combined artificial neural network/residual bilinearization approach for obtaining the second‐order advantage from three‐way non‐linear data , 2005 .

[51]  Florentina Cañada-Cañada,et al.  Nonlinear four-way kinetic-excitation-emission fluorescence data processed by a variant of parallel factor analysis and by a neural network model achieving the second-order advantage: malonaldehyde determination in olive oil samples. , 2008, Analytical chemistry.

[52]  Marcio Pozzobon Pedroso,et al.  Quantitative analysis of essential oils in perfume using multivariate curve resolution combined with comprehensive two-dimensional gas chromatography. , 2011, Analytica chimica acta.

[53]  Yoon-Chang Kim,et al.  Three- and four-way parallel factor (PARAFAC) analysis of photochemically induced excitation-emission kinetic fluorescence spectra. , 2005, The Analyst.

[54]  Hai-Long Wu,et al.  MVC2: A MATLAB graphical interface toolbox for second-order multivariate calibration , 2009 .

[55]  Alejandro C. Olivieri,et al.  Unfolded partial least-squares with residual quadrilinearization: A new multivariate algorithm for processing five-way data achieving the second-order advantage. Application to fourth-order excitation-emission-kinetic-pH fluorescence analytical data , 2011 .

[56]  Graciela M. Escandar,et al.  A review of multivariate calibration methods applied to biomedical analysis , 2006 .

[57]  Marcio Pozzobon Pedroso,et al.  Prediction of the physicochemical properties of gasoline by comprehensive two-dimensional gas chromatography and multivariate data processing. , 2011, Journal of chromatography. A.

[58]  Cristina Ariño,et al.  Development and Possibilities of Multichannel Voltammetric Detection in Liquid Chromatography , 2011 .

[59]  Juan A Arancibia,et al.  Chemometrics-assisted fluorimetry for the rapid and selective determination of heavy polycyclic aromatic hydrocarbons in contaminated river waters and activated sludges. , 2011, Environmental science & technology.

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

[61]  Hadi Parastar,et al.  Resolution and quantification of complex mixtures of polycyclic aromatic hydrocarbons in heavy fuel oil sample by means of GC × GC-TOFMS combined to multivariate curve resolution. , 2011, Analytical chemistry.

[62]  G. M. Mong,et al.  Impurity profiling of a chemical weapon precursor for possible forensic signatures by comprehensive two-dimensional gas chromatography/mass spectrometry and chemometrics. , 2010, Analytical chemistry.

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

[64]  Armando C. Duarte,et al.  Application of Chemometrics in Separation Science , 2006 .

[65]  Alejandro C. Olivieri,et al.  Residual bilinearization combined with kernel-unfolded partial least-squares: A new technique for processing non-linear second-order data achieving the second-order advantage , 2010 .

[66]  Yoon-Chang Kim,et al.  Photocatalytic degradation-excitation-emission matrix fluorescence for increasing the selectivity of polycyclic aromatic hydrocarbon analyses. , 2005, Analytical chemistry.

[67]  I Durán-Merás,et al.  On line photochemically induced excitation-emission-kinetic four-way data: analytical application for the determination of folic acid and its two main metabolites in serum by U-PLS and N-PLS/residual trilinearization (RTL) calibration. , 2008, Analytica chimica acta.

[68]  Hai-Long Wu,et al.  Alternating penalty quadrilinear decomposition algorithm for an analysis of four‐way data arrays , 2007 .

[69]  A. Espinosa-Mansilla,et al.  Determination of marker pteridines in urine by HPLC with fluorimetric detection and second-order multivariate calibration using MCR-ALS , 2011, Analytical and bioanalytical chemistry.

[70]  K. Pierce,et al.  Predicting percent composition of blends of biodiesel and conventional diesel using gas chromatography-mass spectrometry, comprehensive two-dimensional gas chromatography-mass spectrometry, and partial least squares analysis. , 2011, Talanta.

[71]  Gary D. Christian,et al.  Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons , 1980 .

[72]  R. Bro.  Multiway calibration. Multilinear PLS , 1996 .

[73]  Hai-Long Wu,et al.  Alternating penalty trilinear decomposition algorithm for second‐order calibration with application to interference‐free analysis of excitation–emission matrix fluorescence data , 2005 .

[74]  Antonio Segura-Carretero,et al.  Chemometric-assisted MIP-optosensing system for the simultaneous determination of monoamine naphthalenes in drinking waters. , 2009, Talanta.

[75]  M. C. Ortiz,et al.  Quantitative determination in chromatographic analysis based on n-way calibration strategies. , 2007, Journal of chromatography. A.

[76]  Ronei J. Poppi,et al.  Second- and third-order multivariate calibration: data, algorithms and applications , 2007 .

[77]  Robert E Synovec.  Enhancing chemical separations with chemometric data analysis. , 2011, Talanta.

[78]  Santiago A. Bortolato,et al.  Chemometrics-assisted excitation-emission fluorescence spectroscopy on nylon membranes. Simultaneous determination of benzo[a]pyrene and dibenz[a,h]anthracene at parts-per-trillion levels in the presence of the remaining EPA PAH priority pollutants as interferences. , 2008, Analytical chemistry.

[79]  M. P. Callao,et al.  Analytical applications of second-order calibration methods. , 2008, Analytica chimica acta.

[80]  B. W. Wright,et al.  High-speed peak matching algorithm for retention time alignment of gas chromatographic data for chemometric analysis. , 2003, Journal of chromatography. A.

[81]  Andres D Campiglia,et al.  Four-way data coupled to parallel factor model applied to environmental analysis: determination of 2,3,7,8-tetrachloro-dibenzo-para-dioxin in highly contaminated waters by solid-liquid extraction laser-excited time-resolved Shpol'skii spectroscopy. , 2005, Analytical chemistry.

[82]  S. Wold,et al.  Multi‐way principal components‐and PLS‐analysis , 1987 .

[83]  José Manuel Amigo,et al.  ChroMATHography: solving chromatographic issues with mathematical models and intuitive graphics. , 2010, Chemical reviews.

[84]  Jamin C. Hoggard,et al.  Development and application of a comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry method for the analysis of L-beta-methylamino-alanine in human tissue. , 2010, Journal of chromatography. A.

[85]  N. M. Faber,et al.  Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report) , 2006 .

[86]  Klaus Danzer,et al.  Guidelines for calibration in analytical chemistry. Part I. Fundamentals and single component calibration (IUPAC Recommendations 1998) , 1998 .

[87]  Hai-Long Wu,et al.  Excitation-emission-kinetic fluorescence coupled with third-order calibration for quantifying carbaryl and investigating the hydrolysis in effluent water. , 2009, Talanta.

[88]  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 .

[89]  G. M. Escandar,et al.  A novel flow-through fluorescence optosensor for the determination of thiabendazole. , 2007, Analytica chimica acta.

[90]  Marcio Pozzobon Pedroso,et al.  Identification of gasoline adulteration using comprehensive two-dimensional gas chromatography combined to multivariate data processing. , 2008, Journal of chromatography. A.

[91]  J. A. Arancibia,et al.  Second-order advantage achieved with four-way fluorescence excitation-emission-kinetic data processed by parallel factor analysis and trilinear least-squares. Determination of methotrexate and leucovorin in human urine. , 2004, Analytical chemistry.

[92]  Alejandro C Olivieri,et al.  Computing sensitivity and selectivity in parallel factor analysis and related multiway techniques: the need for further developments in net analyte signal theory. , 2005, Analytical chemistry.

[93]  S. Rutan,et al.  Semi-automated alignment and quantification of peaks using parallel factor analysis for comprehensive two-dimensional liquid chromatography-diode array detector data sets. , 2012, Analytica chimica acta.