Target transform, factor analysis

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

Factor rotation by target transformation factor analysis (TTFA)... 

Iterative target transformation factor analysis (ITTFA) is an extension of TTFA and has been introduced by Hopke et al. [12] in environmetrics and by Gemperline [13,14] and Vandeginste et al. [15] in chromatography. The idea behind ITTFA is... 

B.G.M. Vandeginste, F. Leyten, M. Gerritsen, J.W. Noor, G. Kateman and J. Frank, Evaluation of curve resolution and iterative target transformation factor analysis in quantitative analysis by liquid chromatography. J. Chemom., 1 (1987) 57-71. 

P.K. Hopke, D.J. Alpert and B.A. Roscoe, FANTASIA — A program for target transformation factor analysis to apportion sources in environmental samples. Comput. Chem., 7 (1983) 149-155. 

P.J. Gemperline, Target transformation factor analysis with linear inequality constraints applied to spectroscopic-chromatographic data. Anal. Chem., 58 (1986) 2656-2663. 

M.J.P. Gerritsen, H. Tanis, B.G.M. Vandeginste and G. Kateman, Generalized rank annihilation factor analysis, iterative target transformation factor analysis and residual bilinearization for the quantitative analysis of data from liquid-chromatography with photodiode array detection. Anal. Chem., 64 (1992) 2042-2056. 

P.K. Hopke, Tutorial Target transformation factor analysis. Chemom. Intell. Lab. Syst., 6 (1989) 7-19. 

Iterative Target Transform Factor Analysis, ITTFA... 

This algorithm has many aspects similar to Iterative Target Transform Factor Analysis, ITTFA, as discussed in Chapter 5.2.2, and Alternating Least-Squares, ALS as introduced later in Chapter 5.4. The main difference is the inclusion of the window information as provided by the EFA plots. 

Several additional comments are due. As observed in Chapter 5.2.2, Iterative Target Transform Factor Analysis, ITTFA, iterative progress is relatively fast at the beginning and slows down continuously with the number of iterations. The third panel of Figure 5-42 demonstrates that the minimum has not been reached at all after 100 iterations. While the concentration profiles are reasonably well reproduced, there are some problems with the absorption spectra one spectrum has a substantial contribution from another. Nevertheless, considering the simplicity of the algorithm the results are astoundingly accurate. 

ALS should more correctly be called Alternating Linear Least-Squares as every step in the iterative cycle is a linear least-squares calculation followed by some correction of the results. The main advantage and strength of ALS is the ease with which any conceivable constraint can be implemented its main weakness is the inherent poor convergence. This is a property ALS shares with the very similar methods of Iterative Target Transform Factor Analysis, TTTFA and Iterative Refinement of the Concentration Profiles, discussed in Chapters 5.2.2 and 5.3.3. 

PLS (partial least squares) multiple regression technique is used to estimate contributions of various polluting sources in ambient aerosol composition. The characteristics and performance of the PLS method are compared to those of chemical mass balance regression model (CMB) and target transformation factor analysis model (TTFA). Results on the Quail Roost Data, a synthetic data set generated as a basis to compare various receptor models, is reported. PLS proves to be especially useful when the elemental compositions of both the polluting sources and the aerosol samples are measured with noise and there is a high correlation in both blocks. 

The two most widespread statistical receptor models in the literature are regression model of chemical mass balance (CMB) and target transformation factor analysis (TTFA) (. ) The questions to be answered by the receptor models are ... 

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. 

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis. Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented. 

There are two general types of aerosol source apportionment methods dispersion models and receptor models. Receptor models are divided into microscopic methods and chemical methods. Chemical mass balance, principal component factor analysis, target transformation factor analysis, etc. are all based on the same mathematical model and simply represent different approaches to solution of the fundamental receptor model equation. All require conservation of mass, as well as source composition information for qualitative analysis and a mass balance for a quantitative analysis. Each interpretive approach to the receptor model yields unique information useful in establishing the credibility of a study s final results. Source apportionment sutdies using the receptor model should include interpretation of the chemical data set by both multivariate methods. 

It needs to be emphasized at this point that a model is a mathematical representation of the real world. If two models have the same mathematical representation of the real world, they are, in fact, the same model. Chemical mass balance, principal component factor analysis, target transformation factor analysis, etc. have, for all practical purposes. Identical mathematical representations (Equation 1) of the real world and start with the same input data matrices (Figure 4). The principal difference in these "different receptor models is their approach to the solution of either Equation (1) or Equation (2). 

Multivariate methods, on the other hand, resolve the major sources by analyzing the entire ambient data matrix. Factor analysis, for example, examines elemental and sample correlations in the ambient data matrix. This analysis yields the minimum number of factors required to reproduce the ambient data matrix, their relative chemical composition and their contribution to the mass variability. A major limitation in common and principal component factor analysis is the abstract nature of the factors and the difficulty these methods have in relating these factors to real world sources. Hopke, et al. (13.14) have improved the methods ability to associate these abstract factors with controllable sources by combining source data from the F matrix, with Malinowski s target transformation factor analysis program. (15) Hopke, et al. (13,14) as well as Klelnman, et al. (10) have used the results of factor analysis along with multiple regression to quantify the source contributions. Their approach is similar to the chemical mass balance approach except they use a least squares fit of the total mass on different filters Instead of a least squares fit of the chemicals on an individual filter. 

Funke, P.T. Selzer, R.B. Levlnstone, A.R. "FACTANL-Target Transformation Factor Analysis," Quantum Chemistry Program Exchange,... 

The factor analysis technique used was unable to distinguish separate soil and road sources. Ca appeared with Al, Si, K, Ti, and Fe on a factor that can be characterized only as "crustal," including both soil and road materials. It appears that a chemical element balance should always be used as a check on factor analysis results, at least until a more sophisticated factor analysis method, such as target transformation factor analysis (14), can be shown not to require it. 

The only condition for the application of PLS is that several samples are available with known amounts of the compountk of interest, for calibration. Interferences and matrix effects of the unknown compounds have not to be taken into account and do not effect the accurary of the analytical result (see further Section 3.3). The presence of candidate compounds, can be confirmed one at a time by a Target Transformation Factor analysis (TTFA)... 

There are several different iterative algorithms that have been used for SMCR, including alternating least squares (ALS)63 and iterative target transformation factor analysis (ITTFA).64 For more detailed information, the reader is referred to these references. 

The next subsection deals first with aspects common to all resolution methods. These include (1) issues related to the initial estimates, i.e., how to obtain the profiles used as the starting point in the iterative optimization, and (2) issues related to the use of mathematical and chemical information available about the data set in the form of so-called constraints. The last part of this section describes two of the most widely used iterative methods iterative target transformation factor analysis (ITTFA) and multivariate curve resolution-alternating least squares (MCR-ALS). 

Vandeginste, B.G.M., Derks, W., and Kateman, G., Multicomponent self-modeling curve resolution in high performance liquid chromatography by iterative target transformation factor analysis, Anal. Chim. Acta, 173, 253-264, 1985. 

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