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Mathematical improvements to maximum likelihood parallel factor analysis: experimental studies
Author(s) -
VegaMontoto Lorenzo,
Wentzell Peter D.
Publication year - 2005
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.924
Subject(s) - covariance , algorithm , computer science , set (abstract data type) , covariance matrix , experimental data , data set , variety (cybernetics) , statistics , data mining , mathematics , artificial intelligence , programming language
In this paper, the application of a number of simplified algorithms for maximum likelihood parallel factor analysis (MLPARAFAC) to experimental data is explored. The algorithms, described in a companion paper, allow the incorporation of a variety of correlated error structures into the three‐way analysis. In this work, three experimental data sets involving fluorescence excitation‐emission spectra of synthetic three‐component mixtures of aromatic compounds are used to test these algorithms. Different experimental designs were employed for the acquisition of these data sets, resulting in measurement errors that were correlated in either two or three modes. A number of data‐analysis methods were applied to characterize the error structures of these data sets. In all cases, the introduction of statistically meaningful information translated to estimates of better quality than the conventional PARAFAC estimates of concentrations and spectra. The use of the algorithms that employ the error structure suggested by the analysis of the error covariance matrix yielded the best results for each data set. Copyright © 2005 John Wiley & Sons, Ltd.