Principal component analysis application

Malinowski, E.R., Theory of die Distribution of Error Eigenvalues Resulting from Principal Component Analysis with Applications to Spectroscopic Data",... 

K. R. Gabriel, The biplot graphic display of matrices with applications to principal components analysis. Biometrika, 58 (1971) 453-467. 

R. Henrion, N-way principal component analysis. Theory, algorithms and applications. Chemom. Intell. Lab. Syst., 25 (1994) 1-23. 

According to Andersen [12] early applications of LLM are attributed to the Danish sociologist Rasch in 1963 and to Andersen himself. Later on, the approach has been described under many different names, such as spectral map analysis [13,14] in studies of drug specificity, as logarithmic analysis in the French statistical literature [15] and as the saturated RC association model [16]. The term log-bilinear model has been used by Escoufier and Junca [ 17]. In Chapter 31 on the analysis of measurement tables we have described the method under the name of log double-centred principal components analysis. 

R.Tauler and E. Casassas, Application of principal component analysis to the study of multiple equilibria systems — Study of Copper(ll) salicylate monoethanolamine, diethanolamine and triethanolamine systems. Anal. Chim. Acta, 223 (1989) 257-268. 

The application of principal components regression (PCR) to multivariate calibration introduces a new element, viz. data compression through the construction of a small set of new orthogonal components or factors. Henceforth, we will mainly use the term factor rather than component in order to avoid confusion with the chemical components of a mixture. The factors play an intermediary role as regressors in the calibration process. In PCR the factors are obtained as the principal components (PCs) from a principal component analysis (PC A) of the predictor data, i.e. the calibration spectra S (nxp). In Chapters 17 and 31 we saw that any data matrix can be decomposed ( factored ) into a product of (object) score vectors T(nxr) and (variable) loadings P(pxr). The number of columns in T and P is equal to the rank r of the matrix S, usually the smaller of n or p. It is customary and advisable to do this factoring on the data after columncentering. This allows one to write the mean-centered spectra Sq as ... 

NMR alone is insufficient to enable the full assignment of the beer spectra to be made. Application of Principal Component Analysis (PCA) to the spectral profiles of beers of differing type (ales and lagers) showed some distinction on the basis of the aliphatic and sugar compositions, whereas the PCA of the aromatic profiles... 

Yang et al. [389] rapidly distinguished compounds extracted from paper, using on-line SFE-SFC-FHR in conjunction with principal component analysis. The quantitative determination of the surfactant mixture Triton X-100 and other complex oligoether surfactants by means of cSFC-FTIR flow-cells has been reported [390,391]. Practical applications of SFC-FTIR include the determination of nonvolatile compounds from microwave-susceptible packaging that may migrate into heated food. Another application is the analysis of fibre finishes on fibre/textile matrices. 

An important application field of factor and principal component analysis is environmental analysis. Einax and Danzer [1989] used FA to characterize the emission sources of airborne particulates which have been sampled in urban screening networks in two cities and one single place. The result of factor analysis basing on the contents of 16 elements (Al, B, Ba, Cr, Cu, Fe, Mg, Mn, Mo, Ni, Pb, Si, Sn, Ti, V, Zn) determined by Optical Atomic Emission Spectrography can be seen in Fig. 8.17. In Table 8.3 the common factors, their essential loadings, and the sources derived from them are given. 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

The extent of homogeneous mixing of pharmaceutical components such as active drug and excipients has been studied by near-IR spectroscopy. In an application note from NIRSystems, Inc. [47], principal component analysis and spectral matching techniques were used to develop a near-IR technique/algorithm for determination of an optimal mixture based upon spectral comparison with a standard mixture. One advantage of this technique is the use of second-derivative spectroscopy techniques to remove any slight baseline differences due to particle size variations. 

In Chapter 11 some recent approaches for dealing with different aspects of the data reconciliation problem are discussed. A more general formulation in terms of a probabilistic framework is first introduced and its application in dealing with gross error is discussed in particular. In addition, robust estimation approaches are considered, in which the estimators are designed so they that are insensitive to outliers. Finally, an alternative strategy that uses Principal Component Analysis is reviewed. 

As in many such problems, some form of pretreatment of the data is warranted. In all applications discussed here, the analytical data either have been untreated or have been normalized to relative concentration of each peak in the sample. Quality Assurance. Principal components analysis can be used to detect large sample differences that may be due to instrument error, noise, etc. This is illustrated by using samples 17-20 in Appendix I (Figure 6). These samples are replicate assays of a 1 1 1 1 mixture of the standard Aroclors. Fitting these data for the four samples to a 2-component model and plotting the two first principal components (Theta 1 and Theta 2 [scores] in... 

To illustrate the environmental application of the SIMCA method we examined a set of isomer specific analyses of sediment samples. The data examined were derived from more than 200 sediment samples taken from a study site on the Upper Mississippi River (41). These analytical data were transferred via magnetic tape from the laboratory data base to the Cyber 175 computer where principal component analysis were conducted on the isomer concentration data (ug/g each isomer). 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

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