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

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 PM2.5 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.