Parallel factor analysis PARAFAC

Absorption spectra have also been used in the reexamination of pH-dependent color and structural transformations in aqueous solutions of some nonacylated anthocyanins and synthetic flavylium salts." ° In a recent study, the UV-Vis spectra of flower extracts of Hibiscus rosasinensis have been measured between 240 and 748 nm at pH values ranging from 1.1 to 13.0." Deconvolution of these spectra using the parallel factor analysis (PARAFAC) model permitted the study of anthocyanin systems without isolation and purification of the individual species (Figure 2.21). The model allowed identification of seven anthocyanin equilibrium forms, namely the flavylium cation, carbinol, quinoidal base, and E- and Z-chalcone and their ionized forms, as well as their relative concentrations as a function of pH. The spectral profiles recovered were in agreement with previous models of equilibrium forms reported in literature, based on studies of pure pigments. 

Three-way calibrations methods, such as the generalized rank annihilation method (GRAM) and parallel factor analysis (PARAFAC), are becoming increasingly prevalent tools to solve analytical challenges. The main advantage of three-way calibration is estimation of analyte concentrations in the presence of unknown, uncalibrated... 

The parallel factor analysis (PARAFAC) model [18-20] is based on a multilinear model, and is one of several decomposition methods for a multidimensional data set. A major advantage of this model is that data can be uniquely decomposed into individual contributions. Because of this, the PARAFAC model has been widely applied to 3D and also higher dimensional data in the field of chemometrics. It is known that fluorescence data is one example that corresponds well with the PARAFAC model [21]. 

Parallel factor analysis (PARAFAC) (Harshman, 1970 Bro, 1997 Amigo et al., 2010) is a technique that is ideally suited for interpreting multivariate separations data. PARAFAC is a decomposition model for multivariate data which provides three matrices. A, B and C which contain the scores and loadings for each component. The residuals, E, and the number of factors, r, are also extracted. The PARAFAC decomposition finds the best... 

Figure 5.15 The parallel factor analysis (PARAFAC) model for F factors.

Methods for simultaneous Af-way regression can be based on the decomposition of the X array by multiway methods introduced in Section 5.2 (parallel factor analysis (PARAFAC) or Tucker models) and regressing the dependent variable on the components of those models. A drawback with this approach is that the separately estimated components are not necessarily predictive for Y. This caused the development of improved algorithms for multiway regression analysis of that kind. 

Guimet et al. used two potential multiway methods for the discrimination between virgin olive oils and pure olive oils the unfold principal component analysis (U-PCA) and parallel factor analysis (PARAFAC), for the exploratory analysis of these two types of oils. Both methods were applied to the excitation-emission fluorescence matrices (EEM) of olive oils and followed the comparison of the results with the ones obtained with multivariate principal component analysis (PCA) based on a fluorescence spectrum recorded at only one excitation wavelength. 

Finally, an example should be provided about a class of methods, which have also explorative purposes, which will be discussed with more detail and theoretical depth in Chapter 7, that is multiway analysis methods [81]. These methods, among which parallel factor analysis (PARAFAC) will be shown here in action compared to PCA, are to some extent referred to as the conceptual (and mathematical) extension of PCA to arrays of order higher than two. They show their potentiality when the variability of a data set is related to different sources, or conditions, at which a full set of properties for each sample is measured [17-21]. An example, quite common in the food science analysis, is the excitation-emission fluorescence landscape, where, for each sample, an emission spectrum is recorded at each wavelength of the excitation signal. 

Hoggard JC, Synovee RE. Parallel factor analysis (PARAFAC) of target analytes in GC x GC-TOFMS data autranated selectirm of a model with an appropriate number of factors. Anal Chem 2007 79 1611-9. 

The earliest peak nomenclature, and the one still most widely used is that of Coble et al. (1990), which denotes two peaks for humic-like fluorescence, peaks A and C, and one for tyrosine-like fluorescence, peak B. Coble (1996) introduced peaks T (tryptophan-like) and M (marine humic-like). A similar naming scheme was proposed by Parlanti et al. (2000). Since the introduction and expanding use of the multicomponent analysis technique parallel factor analysis (PARAFAC Bro, 1997 Stedmon et al 2003), peak nomenclature has evolved into a numbering scheme based on the output of the model. PARAFAC models have now been developed for diverse environments, both freshwater and marine, and the outputs have resulted in an ever-increasing number of peak designators. 

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