Comparison of a new variant of PMF with other receptor modeling methods using artificial and real sediment PCB data sets

Abstract

SUMMARYA 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.

PCBs in Great Lakes sediments, determined by positive matrix factorization

“…A more detailed description of the PMF model can be found in Bzdusek (2005), Bzdusek and Christensen (2006), and Bzdusek et al (2006a). The PMF solutions incorporate weighting of individual data points so that both high and low pollutant concentrations will be modeled accurately (Bzdusek et al, 2006b;Bzdusek and Christensen, 2006). In all cases, results are the average with standard deviations of means for 10 PMF runs with the same data matrix.…”

“…The model minimizes a weighted sum of squares of differences between calculated and measured elements of the data matrix by normal equations and uses rotations based on the non-negative least squares (NNLS) procedure to eliminate negative elements of G and F. The data matrix X is initially average scaled by dividing the PCB congener concentrations in each sediment sample by their respective average concentration for all samples and then backscaled (multiply by averages) after rotations. A more detailed description of the PMF model can be found in Bzdusek (2005), Bzdusek and Christensen (2006), and Bzdusek et al (2006a). The PMF solutions incorporate weighting of individual data points so that both high and low pollutant concentrations will be modeled accurately (Bzdusek et al, 2006b;Bzdusek and Christensen, 2006).…”

“…PMF has shown to be especially well suited to determine factors of low contributions such as the ones from an original Aroclor mix in a strongly dechlorinating environment (Bzdusek and Christensen, 2006). The reason for this may be linked to the weighting of elements of the data matrix in the least squares objective function with the inverse of standard deviations of the values.…”

Source apportionment of PAHs in surface sediments using positive matrix factorization combined with GIS for the estuarine area of the Yangtze River, China

“…PMF offers an additional advantage over PCA because of its superior ability to handle missing values and to account for data precision and because it does not rely on previous knowledge of sources by direct measurement or from emission inventories (Vaccaro et al, 2007;Comero et al, 2011). This method has been applied in source analysis of atmospheric pollution in particulate matter, heavy metal pollution in soil and water sediments, and the study of wet deposition (Chueinta et al, 2000;Bzdusek and Christensen, 2006;Keeler et al, 2006;Comero et al, 2012).…”

Hazard Ranking of Wastewater Sources in a Highly Polluted River in Northern Taiwan by Using Positive Matrix Factorization With Metal Elements

“…(3) it does not need to be orthogonal, which makes the formed factors close to real profile of pollution sources; (4) it quantifies source contributions; and (5) the factors are not excessively influenced by outliers [24][25][26]. However, in most of these studies, source apportionment was estimated using spatial samplings, which neglected temporal variation in the source contributions.…”