Comparison of different multiway methods for the analysis of geographical metal distributions in fish, sediments and river waters in Catalonia

Comparison of different multiway data analysis methods based on Principal Component Analysis and Multivariate Curve Resolution Matrix Augmentation bilinear models and on PARAFAC and TUCKER3 models is performed in the analysis of a three-way data set built up by the analysis of 11 metal ions in 17 fish, sediment and water samples from the same river site locations of Catalonia (NE, Spain). Adaptation of Multivariate Curve Resolution to PARAFAC and TUCKER3 type of models showed the flexibility of this method to handle different data structures and also to fulfill different constraint types. Although the way the results were obtained using these different chemometric methods varied, similar environmental interpretations and conclusions were derived independently of the chemometric method used for data analysis.

[1]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

[2]  Damià Barceló,et al.  Multivariate correlation between concentrations of selected herbicides and derivatives in outflows from selected U.S. Midwestern reservoirs , 2000 .

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

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

[5]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[6]  R. Henrion.  N-WAY PRINCIPAL COMPONENT ANALYSIS : THEORY, ALGORITHMS AND APPLICATIONS , 1994 .

[7]  Gene H. Golub,et al.  Matrix computations , 1983 .

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

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

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

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

[12]  Philip K. Hopke,et al.  Discarding or downweighting high-noise variables in factor analytic models , 2003 .

[13]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[14]  Rasmus Bro,et al.  Improving the speed of multi-way algorithms:: Part I. Tucker3 , 1998 .

[15]  R. Henry,et al.  Extension of self-modeling curve resolution to mixtures of more than three components: Part 1. Finding the basic feasible region , 1990 .

[16]  Philip K. Hopke,et al.  The chemical mass balance as a multivariate calibration problem , 1997 .

[17]  D. Massart,et al.  Dealing with missing data: Part II , 2001 .

[18]  C. Harris.  Problems in measuring change , 1965 .

[19]  J. Leeuw,et al.  Principal component analysis of three-mode data by means of alternating least squares algorithms , 1980 .

[20]  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 .

[21]  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.

[22]  D. Burdick.  An introduction to tensor products with applications to multiway data analysis , 1995 .

[23]  P. Paatero,et al.  Analysis of different modes of factor analysis as least squares fit problems , 1993 .

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

[25]  P. Hopke.  An introduction to receptor modeling , 1991 .

[26]  H. Kiers.  Towards a standardized notation and terminology in multiway analysis , 2000 .

[27]  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.

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

[29]  Ashutosh Kumar Singh,et al.  Treatment of nondetects in multivariate analysis of groundwater geochemistry data , 2002 .

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

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

[32]  Age K. Smilde,et al.  Constrained three‐mode factor analysis as a tool for parameter estimation with second‐order instrumental data , 1998 .

[33]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

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

[35]  S. D. Jong,et al.  Handbook of Chemometrics and Qualimetrics , 1998 .

[36]  I. Jolliffe.  Principal Component Analysis , 2002 .

[37]  R. Brereton.  Chemometrics in Environmental Chemistry , 1995 .

[38]  D. Massart,et al.  Dealing with missing data , 2001 .