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Comparison of a new variant of PMF with other receptor modeling methods using artificial and real sediment PCB data sets
Author(s) -
Bzdusek Philip A.,
Christensen Erik R.
Publication year - 2006
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.777
Subject(s) - set (abstract data type) , data set , mathematics , least squares function approximation , eigenvalues and eigenvectors , statistics , matrix (chemical analysis) , computer science , algorithm , chemistry , chromatography , physics , quantum mechanics , estimator , programming language
A new variant of positive matrix factorization (PMF) is developed and compared to existing methods of PMF and eigenvalue‐based factor analysis (FA) using an artificially created data set, including environmental variability and an environmental data set. Diagnostic tools are considered for the determination of the number of significant factors for all methods. The methodology for the new method of PMF is based on a nonnegative least squares (NNLS) technique combined with iterative rotations to eliminate negative elements from the source profile and source contribution matrices. The PMF and FA methods reproduce the source profiles for the artificial data set well, and the PMF method provides realistic source profiles for the real data set, whereas the FA method does not. The new method may be able to reproduce zero values better than PMF using penalty terms, and also appears to provide a better fit for the data since the minimum value of the weighted sum of squares of residuals Q is maintained during the rotations. Copyright © 2005 John Wiley & Sons, Ltd.