Principle component method

The number of absorbing species in solution in spectrophotometry can be estimated by factor analysis or principle component method (PCM) especially. Sometimes, the term eigenvalues analysis is also used. The method is traditionally used in spectrophotometry. Because of the simplicity of spectrophotometry, a detailed description is given here even though this method is not frequently used in extraction studies. 

In a study of performance measurement related to lean manufacturing that affects net profit of SMEs in the manufacturing sector in Thailand, the researchers used factor analysis to find the factors. The study extracted factors using the principle component method and forecasted identify factors that affect net profit by using multinomial logistic regression analysis and grouping patterns of business operations of SMEs with statistical analysis. 

On the other hand, techniques like Principle Component Analysis (PCA) or Partial Least Squares Regression (PLS) (see Section 9.4.6) are used for transforming the descriptor set into smaller sets with higher information density. The disadvantage of such methods is that the transformed descriptors may not be directly related to single physical effects or structural features, and the derived models are thus less interpretable. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Two-component methods represent the most widely applied principles in sulfone syntheses, including C—S bond formation between carbon and RSOz species of nucleophilic, radical or electrophilic character as well as oxidations of thioethers or sulfoxides, and cheletropic reactions of sulfur dioxide. Three-component methods use sulfur dioxide as a binding link in order to connect two carbons by a radical or polar route, or use sulfur trioxide as an electrophilic condensation agent to combine two hydrocarbon moieties by a sulfonyl bridge with elimination of water. 

Since in many applications minor absorption changes have to be detected against strong, interfering background absorptions of the matrix, advanced chemometric data treatment, involving techniques such as wavelet analysis, principle component analysis (PCA), partial least square (PLS) methods and artificial neural networks (ANN), is a prerequisite. 

Chemometric evaluation methods can be applied to the signal from a single sensor by feeding the whole data set into an evaluation program [133,135]. Both principle component analysis (PCA) and partial least square (PLS) models were used to evaluate the data. These are chemometric methods that may be used for extracting information from a multivariate data set (e.g., from sensor arrays) [135]. The PCA analysis shows that the MISiC-FET sensor differentiates very well between different lambda values in both lean gas mixtures (excess air) and rich gas mixtures (excess fuel). The MISiC-FET sensor is seen to behave as a linear lambda sensor [133]. It... 

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. 

The experimental studies of three-component systems based on phase equilibria follow the same principles and methods discussed for two-component systems. The integral form of the equations remains the same. The added complexity is the additional composition variable the excess chemical potentials become functions of two composition variables, rather than one. Because of the similarity, only those topics that are pertinent to ternary systems are discussed in this section of the chapter. We introduce pseudobinary systems, discuss methods of determining the excess chemical potentials of two of the components from the experimental determination of the excess chemical potential of the third component, apply the set of Gibbs-Duhem equations to only one type of phase equilibria in order to illustrate additional problems that occur in the use of these equations, and finally discuss one additional type of phase equilibria. 

Raamsdonk and colleagues set out to develop a metabolomics method that could be used to characterize proteins of unknown function in yeast [14]. Using an NMR approach they analyzed intracellular metabolites in mutants of Saccharomyces cerevisiae. The resulting NMR spectra were then analyzed by multivariate analysis, including principle component analysis (PCA) to identify differences in the spectra that can distinguish different mutants (Fig. 2). Two important results came out of these studies that would reveal the value of metabolomics in biological research. 

Fig. 2 NMR-based metabolomics can be used to quickly identify changes in the global NMR pattern. In this case, the red peaks between 2.5-0.5 ppm are indicative of metabolic differences that are specific to the disease state. Actual data is not nearly as clear as this schematic. The analysis of typical NMR metabolomics datasets requires the use of multivariate analysis methods, such as principle components analysis (PCA), in order to use the metabolome to classify samples...

In the so-called direct assay format, a biotinylated component binds to an antibody directly coupled to acceptor beads or to a protein captured by this antibody (Figure 8.4A). In the indirect assay format, the antibody used for capturing the biomolecule is in turn bound by a secondary antibody or by Protein A conjugated to the acceptor beads. In principle, any method capable of capturing the interaction partners to donor and acceptor beads, respectively, is suitable for setting up an AlphaScreen assay. 

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