## 4 Multivariate Analysis for Source Apportionment of Water-Soluble OA  
Regardless of the sophisticated and high-resolution multidimensional analytical techniques employed in the water-soluble OA analysis, the quality of the results is always dependent on the capacity to extract useful information from the acquired data. Yet, the processing and treatment of the data acquired by many of the multidimensional techniques presented in this review is not a trivial task. Some of these techniques can provide information regarding hundreds or even thousands of different compounds, which may cause a severe overlap of the different analytical signals obtained from a complex sample. Inaddition, the data produced by these techniques, especially when combined with chromatographic techniques, may easily exceed more than three or four analytical dimensions. Indeed, nowadays, one of the biggest limitations to a wide application of these advanced instrumental approaches is the lack of knowledge, and analytical expertise for interpreting the huge and complex data sets produced [43]. This lack of knowledge associated with the chemical complexity of the aerosol WSOM has limited the study of this matrix to the identification of some target components, the identification of functional chemical groups, and the assignment of sources and temporal characteristic patterns. In this sense, almost all applications of chemometric tools to the study of aerosol WSOM have been focused on mining the acquired data for highlighting different patterns that may be associated with source profiles and source contributions-the so-called source apportionment methodologies. There are several source apportionment methodologies already in use, namely the chemical mass balance (CMB) and chemical transport model (CTM), as well as some multivariate factor analysis methodologies, such as principal component analysis (PCA), PMF, and multivariate curve resolution-alternating least squares (MCR-ALS) (e.g., references [87; 88; 89; 90] and references therein). The CMB model uses compounds associated with specific sources as references (e.g., levoglucosan as a tracer of biomass burning) to identify the contribution of that particular source. Therefore, the CMB model is mainly limited to the study of well-known emission source profiles [87; 89]. The CTM requires descriptions of the main chemical and physical processes driving air concentration of primary and secondary pollutants, such as sulfur and nitrogen oxides, ozone, and atmospheric PM, being used for investigating and assessing ambient air quality at various spatial and temporal scales (reference [90] and references therein). On the other hand, multivariate factor analysis methodologies allow identifying profiles from experimental data based on numerical factors. Although not corresponding to a particular spectrum of a pure chemical compound, these factors may be related to emission sources and/or functional chemical groups. As pointed out by [PERSON] et al. [87], the MCR-ALS and PMF provide similar results, whereas the PCA methodology produces profiles with the weakest physical meaning. An example of the application of these methods to the study of water-soluble OA is the recent work presented by [PERSON] et al. [35], in which MCR-ALS was applied to \({}^{1}\)H NMR data of WSOM from atmospheric aerosols. In this work, the authors were able to identify a total of five factors: two factors were associated with chemical tracers of marine SOA and biogenic sources (e.g., methane-sulphonic acids and low-molecular-weight amines); other two factors were associated with \"aged\" components (one, of which was also associated with aged biomass-burning particles); and the fifth factor was associated with primary wood-burning particles and showed a chemical composition dominated by anhydrosugars, other polyols, and phenolic compounds [35]. This study also showed an agreement between these factors and the results derived from PMF analysis of the AMS data [35].