Target factor transformation

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. 

Harrington, P. B. Voorhees, K. J. Franco, B. Hendricker, A. D. Validation using sensitivity and target transform factor analyses of neural network models for classifying bacteria from mass spectra. J. Am. Soc. Mass Spectrom. 2002,13,10-21. 

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. 

Factor analysis extracts information from the sample data set (e.g., IR spectra) and does not rely on reference minerals. However, because abstract factors have no physical meaning, reference minerals may be needed in target transformations or other procedures to extract mineralogical information. One valuable piece of information obtainable without the use of extraneous data is the number of components required to represent the data within experimental error. Reported applications of factor analysis to mineralogy by FTIR are few (12). However, one commercial laboratory is offering routine FTIR mineral analyses to the petroleum industry, based on related methods (22). 

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. 

Results For the St. Louis data, the target transformation analysis results for the fine fraction without July Uth and 5th are given in table 6. The presence of a motor vehicle source, a sulfur source, a soil or flyash source, a titanium source, and a zinc source are indicated. The sulfur, titanium and zinc factors were determined from the simple initial test vectors for those elements. The concentration of sulfur was not related to any other elements and represents a secondary sulfate aerosol resulting from the conversion of primary sulfur oxide emissions. Titanium was found to be associated with sulfur, calcium, iron, and barium. Rheingrover ( jt) identified the source of titanium as a paint-pigment factory located to the south of station 112. The zinc factor, associated with the elements chlorine, potassium, iron and lead, is attributed to refuse incinerator emissions. This factor could also represent particles from zinc and/or lead smelters, though a high chlorine concentration is usually associated with particles from refuse incinerators ( ). The sulfur concentration in the refined sulfate factor is consistent with that of ammonium sulfate. The calculated lead concentration in the motor vehicle factor of ten percent and a lead to bromine ratio of about 0.28 are typical of values reported in the literature (25). The concentration of lead in... 

Roscoe, B. A. Hopke, P. K. Comparison of Weighted and Unweighted Target Transformation Rotations in Factor Analysis, Computers and Chemistry, in press,... 

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. 

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