A holistic approach combining factor analysis, positive matrix factorization, and chemical mass balance applied to receptor modeling

Abstract

Rapid urbanization and population growth resulted in severe deterioration of air quality in most of the major cities in India. Therefore, it is essential to ascertain the contribution of various sources of air pollution to enable us to determine effective control policies. The present work focuses on the holistic approach of combining factor analysis (FA), positive matrix factorization (PMF), and chemical mass balance (CMB) for receptor modeling in order to identify the sources and their contributions in air quality studies. Insight from the emission inventory was used to remove subjectivity in source identification. Each approach has its own limitations. Factor analysis can identify qualitatively a minimal set of important factors which can account for the variations in the measured data. This step uses information from emission inventory to qualitatively match source profiles with factor loadings. This signifies the identification of dominant sources through factors. PMF gives source profiles and source contributions from the entire receptor data matrix. The data from FA is applied for rank reduction in PMF. Whenever multiple solutions exist, emission inventory identifies source profiles uniquely, so that they have a physical relevance. CMB identifies the source contributions obtained from FA and PMF. The novel approach proposed here overcomes the limitations of the individual methods in a synergistic way. The adopted methodology is found valid for a synthetic data and also the data of field study.

Contribution of polycyclic aromatic hydrocarbon (PAH) sources to the urban environment: A comparison of receptor models

“…The main reason for these disagreements is the different theoretical approaches of the models. The differences in the results obtained from the different models emphasize the sensitivity of the methods to the accuracy of the receptor concentration and source profile used from the emission inventory (Selvaraju et al, 2013). To combine the advantages and disadvantages of receptor models (e.g.…”

Integrated Application of Multivariate Statistical Methods to Source Apportionment of Watercourses in the Liao River Basin, Northeast China

“…The number of source factors should be calculated before running the PMF model [17,18]. Considering the Q Value, the number of source factors for PMF was set to five for three groups (groups A, B and C).…”

“…Compared with PCA, PMF could further quantitatively analyze different pollution sources [17]. However, the results obtained via the PMF method might introduce uncertainty into the conclusions [18,52]. The assessment of source apportionment by the PMF model must be confirmed via PCA to improve its reliability; to a certain extent, the PCA model is the foundation of the PMF, and the PMF model provides more details and expands upon the PCA; the combination of the two methods can provide more valuable information [17,18,52,53].…”

“…PMF is a multivariate factorization model based on a least squares approach, using a data point weighting method [17,18]. The model can be written as follows in Equation (1): $X_{ij}={\sum }_{k=1}^p{g}_{ik}{f}_{kj}+e_{ij}$ where X ij represents the elements of the input data matrix of i (number of samples) by j (chemical species) dimensions; g ik represents the elements of the factor scores; f kj represents the factor-loading matrices; e ij is the residual for each sample/species; and p is the number of factors.…”

“…Principal component analysis (PCA) and factor analysis (FA) have been used to determine latent sources of pollution, while effectively reducing data dimensionality with minimal loss of meaningful information and grouping multiple variables according to their common characteristics in studies on water environments [4,6,15,16]. The positive matrix factorization (PMF) approach has been successfully used to quantitatively apportion concentrations to their sources [17] and demarcate major sources of pollution [18]. …”