Parallel Factor Analysis: Trilinear Data

In this chapter the processing of trilinear three-way data is discussed, using the most popular algorithm for this task, i.e., parallel factor analysis. The MATLAB graphical interface software MVC2 is employed for data processing, including analyte determination in samples where unexpected constituents occur (i.e., exploiting the second-order advantage). If the chapter reading is followed by simultaneously running the software as indicated, several important aspects of the multiway calibration procedure of second-order data for analyte quantitation can be easily grasped: (1) the process of decomposing the three-way array of signals, (2) the selection of the analyte profile among all the retrieved profiles in the different data modes, (3) the construction of the so-called pseudo-univariate calibration plot for the analyte of interest, and (4) the prediction of the concentration of the analyte in a given sample from the latter plot with its corresponding analytical figures of merit.

[1]  Hai-Long Wu,et al.  An alternating trilinear decomposition algorithm with application to calibration of HPLC–DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons , 1998 .

[2]  Alejandro C Olivieri,et al.  Chemometric resolution of fully overlapped CE peaks: Quantitation of carbamazepine in human serum in the presence of several interferences , 2008, Electrophoresis.

[3]  Jinliang Huang,et al.  Effects of changing land use on dissolved organic matter in a subtropical river watershed, southeast China , 2012, Regional Environmental Change.

[4]  P. Paatero.  A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis , 1997 .

[5]  R. Sleighter,et al.  Molecular characterization of dissolved organic matter (DOM) along a river to ocean transect of the lower Chesapeake Bay by ultrahigh resolution electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry , 2008 .

[6]  L. Buydens,et al.  Warping methods for spectroscopic and chromatographic signal alignment: a tutorial. , 2013, Analytica chimica acta.

[7]  D. McKnight,et al.  Fluorescence spectroscopy reveals ubiquitous presence of oxidized and reduced quinones in dissolved organic matter. , 2005, Environmental science & technology.

[8]  L. Tranvik,et al.  Photochemical production of ammonium and transformation of dissolved organic matter in the Baltic Sea , 2007 .

[9]  K. Murphy,et al.  Distinguishing between terrestrial and autochthonous organic matter sources in marine environments using fluorescence spectroscopy , 2008 .

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

[11]  Treavor H. Boyer,et al.  Behavior of reoccurring PARAFAC components in fluorescent dissolved organic matter in natural and engineered systems: a critical review. , 2012, Environmental science & technology.

[12]  J. Lapierre,et al.  Effects of macrophytes and terrestrial inputs on fluorescent dissolved organic matter in a large river system , 2009, Aquatic Sciences.

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

[14]  M. A. Herrador,et al.  Intra-laboratory testing of method accuracy from recovery assays. , 1999, Talanta.

[15]  Arthur Charles Clarke,et al.  Profiles of the Future : An Inquiry into the Limits of the Possible , 1999 .

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

[17]  P. Massicotte,et al.  Spatial connectivity in a large river system: resolving the sources and fate of dissolved organic matter. , 2011, Ecological applications : a publication of the Ecological Society of America.

[18]  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 .

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

[20]  W. Dunsmuir,et al.  Optimized parameters for fluorescence-based verification of ballast water exchange by ships. , 2006, Environmental science & technology.

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

[22]  R. Jaffé,et al.  Optical characterization of dissolved organic matter in tropical rivers of the Guayana Shield, Venezuela , 2010 .

[23]  M. C. Ortiz,et al.  Optimization of a GC/MS procedure that uses parallel factor analysis for the determination of bisphenols and their diglycidyl ethers after migration from polycarbonate tableware. , 2013, Talanta.

[24]  Luiz Antonio Fonseca de Godoy,et al.  Determination of fuel origin by comprehensive 2D GC-FID and parallel factor analysis , 2013 .

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

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

[27]  R. Bro,et al.  A new efficient method for determining the number of components in PARAFAC models , 2003 .

[28]  P. Raymond,et al.  Inputs of fossil carbon from wastewater treatment plants to U.S. rivers and oceans. , 2009, Environmental science & technology.

[29]  B. Bergamaschi,et al.  Evaluation of specific ultraviolet absorbance as an indicator of the chemical composition and reactivity of dissolved organic carbon. , 2003, Environmental science & technology.

[30]  M. Xenopoulos,et al.  Unraveling the role of land use and microbial activity in shaping dissolved organic matter characteristics in stream ecosystems , 2010 .

[31]  José Barbosa,et al.  A multiway approach for classification and characterization of rabbit liver apothioneins by CE‐ESI‐MS , 2008, Electrophoresis.

[32]  Graciela M. Escandar,et al.  Time-alignment of bidimensional chromatograms in the presence of uncalibrated interferences using parallel factor analysis: Application to multi-component determinations using liquid-chromatography with spectrofluorimetric detection , 2010 .

[33]  W. Cooper,et al.  Characterization of dissolved organic matter fluorescence in the South Atlantic Bight with use of PARAFAC model: Relationships between fluorescence and its components, absorption coefficients and organic carbon concentrations , 2010 .

[34]  J. Berge,et al.  Partial uniqueness in CANDECOMP/PARAFAC , 2004 .

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