Ziad Ramadan

Understanding and controlling rotations in factor analytic models

Abstract Positive Matrix Factorization (PMF) is a least-squares approach for solving the factor analysis problem. It has been implemented in several forms. Initially, a program called PMF2 was used. Subsequently, a new, more flexible modeling tool, the Multilinear Engine, was developed. These programs can utilize different approaches to handle the problem of rotational indeterminacy. Although both utilize non-negativity constraints to reduce rotational freedom, such constraints are generally insufficient to wholly eliminate the rotational problem. Additional approaches to control rotations are discussed in this paper: (1) global imposition of additions among “scores” and subtractions among the corresponding “loadings” (or vice versa), (2) constraining individual factor elements, either scores and/or loadings, toward zero values, (3) prescribing values for ratios of certain key factor elements, or (4) specifying certain columns of the loadings matrix as known fixed values. It is emphasized that application of these techniques must be based on some external information about acceptable or desirable shapes of factors. If no such a priori information exists, then the full range of possible rotations can be explored, but there is no basis for choosing one of these rotations as the “best” result. Methods for estimating the rotational ambiguity in any specific result are discussed.

IDENTIFICATION OF SOURCES OF PHOENIX AEROSOL BY POSITIVE MATRIX FACTORIZATION

ABSTRACT Chemical composition data for fine and coarse particles collected in Phoenix, AZ, were analyzed using positive matrix factorization (PMF). The objective was to identify the possible aerosol sources at the sampling site. PMF uses estimates of the error in the data to provide optimum data point scaling and permits a better treatment of missing and below-detection-limit values. It also applies nonnegativity constraints to the factors. Two sets of fine particle samples were collected by different samplers. Each of the resulting fine particle data sets was analyzed separately. For each fine particle data set, eight factors were obtained, identified as (1) biomass burning characterized by high concentrations of organic carbon (OC), elemental carbon (EC), and K; (2) wood burning with high concentrations of Na, K, OC, and EC; (3) motor vehicles with high concentrations of OC and EC; (4) nonferrous smelting process characterized by Cu, Zn, As, and Pb; (5) heavy-duty diesel characterized by high EC, OC, and Mn; (6) sea-salt factor dominated by Na and Cl; (7) soil with high values for Al, Si, Ca, Ti, and Fe; and (8) secondary aerosol with SO4 -2 and OC that may represent coal-fired power plant emissions. For the coarse particle samples, a five-factor model gave source profiles that are attributed to be (1) sea salt, (2) soil, (3) Fe source/motor vehicle, (4) construction (high Ca), and (5) coal-fired power plant. Regression of the PM mass against the factor scores was performed to estimate the mass contributions of the resolved sources. The major sources for the fine particles were motor vehicles, vegetation burning factors (biomass and wood burning), and coal-fired power plants. These sources contributed most of the fine aerosol mass by emitting carbonaceous particles, and they have higher contributions in winter. For the coarse particles, the major source contributions were soil and construction (high Ca). These sources also peaked in winter.

Comparison of Positive Matrix Factorization and Multilinear Engine for the source apportionment of particulate pollutants

Abstract New approaches to solving the factor analysis (FA) problem have recently been developed by recognizing that factor analysis is fundamentally a least-squares (LS) problem. This approach is called Positive Matrix Factorization (PMF). Two programs have been written to implement different algorithms for solving the problem. These programs are PMF2 and Multilinear Engine (ME-2). The two programs use different algorithms to obtain the least-squares solution and the constraints are imposed in different ways. Elemental composition data for particle samples collected in Phoenix, AZ from June 1996 through June 1998, were used to compare the source apportionment of these two programs. The ME-2 results presented in this paper are compared with the previously published PMF2 results. The identification of the eight PMF sources returned one questionable source: wood burning and some peculiar mass contributions. The extra features of ME-2 made it possible to also investigate the sources responsible for the fine particles. The mixed-way approach indicated the existence of incinerators in the Phoenix area. Like PMF, ME-2 identified high source contributions for biomass burning, motor vehicles (with higher contribution in winter), coal-fired power plants (secondary particles with higher contributions in summer), soil, and nonferrous smelting process. Sea salt and heavy-duty diesel were identified by the ME two-way analysis, but they disappeared in the three-way analysis of the dual fine particle sequential sampler (DFPSS) and DICHOT data. Instead, an obvious incinerator source was identified again. Thus, PMF and ME-2 identified the same major sources responsible for the PM 2.5 in Phoenix, but some of the sources identified by PMF2 appear to be uncertain. The three-way analysis provided additional information about possible sources, but also returned unexplainable sources.

Receptor modeling of ambient and personal exposure samples: 1998 Baltimore Particulate Matter Epidemiology-Exposure Study

Sources of particulate matter exposure for an elderly population in a city north of Baltimore, MD were evaluated using advanced factor analysis models. Data collected with versatile air pollutant samplers positioned at a community site, outside and inside of an elderly residential facility were analyzed with a three-way analysis to identify the source(s) that contributed to all sample types. These sources were secondary sulfate, secondary nitrate, motor vehicles, and a organic carbon (OC). The OC source contained 96% OC and most likely represents positive volatile organic carbon artifact and other unidentified sources. No soil source was found that contributed significantly to these samples. A second set of data was collected with personal samplers (PEM) from 10 elderly subjects, their apartments, a central indoor location, and outdoors. The PEM data were analyzed using a complex model with a target for soil that included factors that are common to all of the types of samples (external factors) and factors that only apply to the data from the individual and apartment samples (internal factors). From these results, the impact of outdoor sources and indoor sources on indoor concentrations were assessed. The identified external factors were sulfate, soil, and an unknown factor. Internal factors were identified as gypsum or wall board, personal care products, and a factor representing variability not explained by the other indoor sources. The latter factor had a composition similar to outdoor particulate matter and explained 36% of the personal exposure. External factors contributed 63% to personal exposure with the largest contribution from sulfate (48%).

Variable selection in classification of environmental soil samples for partial least square and neural network models

Abstract Two variable selection methods were evaluated by comparing their predictions with respect to differentiating among environmental soil samples. The focus of this work is to determine which input variables are most relevant for prediction of soil sources using discriminant partial least square (D-PLS) and back-propagation artificial neural network (BP-ANN) models. The methods investigated were stepwise variable selection method and genetic algorithms (GAs). Microbial community DNA was extracted from 48 environmental soil samples derived from different field crops and soil sources. After amplification of bacterial ribosomal RNA genes by polymerase chain reaction (PCR), the products were separated by gel electrophoresis. Characteristic complex band patterns were obtained, indicating high bacterial diversity. Two hundred and twenty-three DNA band patterns produced in the gels of the soil samples were used in the analysis, after removal of included DNA standard markers. Based on the brightness of the bands, densitometric curves of the selected DNA band pattern were extracted from the gel images. The curves were smoothed using Savitsky–Golay method and scaled to the DNA standard markers. The prediction results based on the two variable selection methods for PLS and ANN models are presented and compared. Both methods gave good results before any variable selection methods, with the ANN being better than D-PLS. The prediction performance of both methods specially the D-PLS were improved by applying the stepwise variable selection and the GA variable selection method. The study also shows that GA variable selection had a significant improvement of the predictive ability than the stepwise variable selection method.