Principal component analysis, analytical methods

One of the main attractions of normal mode analysis is that the results are easily visualized. One can sort the modes in tenns of their contributions to the total MSF and concentrate on only those with the largest contributions. Each individual mode can be visualized as a collective motion that is certainly easier to interpret than the welter of information generated by a molecular dynamics trajectory. Figure 4 shows the first two normal modes of human lysozyme analyzed for their dynamic domains and hinge axes, showing how clean the results can sometimes be. However, recent analytical tools for molecular dynamics trajectories, such as the principal component analysis or essential dynamics method [25,62-64], promise also to provide equally clean, and perhaps more realistic, visualizations. That said, molecular dynamics is also limited in that many of the functional motions in biological molecules occur in time scales well beyond what is currently possible to simulate. 

Multivariate chemometric techniques have subsequently broadened the arsenal of tools that can be applied in QSAR. These include, among others. Multivariate ANOVA [9], Simplex optimization (Section 26.2.2), cluster analysis (Chapter 30) and various factor analytic methods such as principal components analysis (Chapter 31), discriminant analysis (Section 33.2.2) and canonical correlation analysis (Section 35.3). An advantage of multivariate methods is that they can be applied in... 

Musumarra et al. [43] identified miconazole and other drugs by principal components analysis of standardized thin-layer chromatographic data in four eluent systems. The eluents, ethylacetate methanol 30% ammonium hydroxide (85 10 15), cyclohexane-toluene-diethylamine (65 25 10), ethylacetate chloroform (50 50), and acetone with the plates dipped in potassium hydroxide solution, provided a two-component model that accounts for 73% of the total variance. The scores plot allowed the restriction of the range of inquiry to a few candidates. This result is of great practical significance in analytical toxicology, especially when account is taken of the cost, the time, the analytical instrumentation and the simplicity of the calculations required by the method. 

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 following discussion, three types of air pollutant analytical data will be examined using principal component analysis and the K-Nearest Neighbor (KNN) procedure. A set of Interlaboratory comparison data from X-ray emission trace element analysis, data from a comparison of two methods for determining lead In gasoline, and results from gas chromatography/mass spectrometry analysis for volatile organic compounds In ambient air will be used as Illustrations. 

Various approaches can be taken for constructing the U matrix. With PCR, a principal components analysis is used because PCA is an efficient method for finding linear combinations of variables that describe variation in the row space of R (See Section 4.2.2). With analytical chemistry data, it is usually possible to describe the variation in R using significantly fewer PCs than the number of original variables. This small number of columns effectively eliminates the matrix inversion problem. 

Other strong advantages of PCR over other methods of calibration are that the spectra of the analytes have not to be known, the number of compounds contributing to the signal have not to be known on the beforehand, and the kind and concentration of the interferents should not be known. If interferents are present, e.g. NI, then the principal components analysis of the matrix, D, will reveal that there are NC = NA -I- NI significant eigenvectors. As a consequence the dimension of the factor score matrix A becomes (NS x NC). Although there are NC components present in the samples, one can suffice to relate the concentrations of the NA analytes to the factor score matrix by C = A B and therefore, it is not necessary to know the concentrations of the interferents. 

Irrespective of the method chosen, meaningful data can only be obtained if the appropriate level of signal to noise (S/N) is reached in the spectrum of each analyte. This has been achieved for Raman measurements through short data acquisition times (<1 s) and application of mathematical approaches such as If-harmonic means clustering (KHMC), factor analysis [57] and principal component analysis (PCA) [58] to the data set. Ultimately the sample response to the excitation energy determines the speed that a measurement can be made. 

Thielemans, A. and Massart, D.L., The use of principal component analysis as a display method in the interpretation of analytical chemical, biochemical, environmental, and epidemiological data, Chimia, 39, 236-242, 1985. 

There are several chemometric methods applicable which provide numerical analytical data and their implementation remains a specialist affair. They vary from simple statistical tools such as principal component analysis (PCA) to highly complex methods such as neural networks. 

NIR spectroscopy became much more useful when the principle of multiple-wavelength spectroscopy was combined with the deconvolution methods of factor and principal component analysis. In typical applications, partial least squares regression is used to model the relation between composition and the NIR spectra of an appropriately chosen series of calibration samples, and an optimal model is ultimately chosen by a procedure of cross-testing. The performance of the optimal model is then evaluated using the normal analytical performance parameters of accuracy, precision, and linearity. Since its inception, NIR spectroscopy has been viewed primarily as a technique of quantitative analysis and has found major use in the determination of water in many pharmaceutical materials. 

A general requirement for P-matrix analysis is n = rank(R). Unfortcmately, for most practical cases, the rank of R is greater than the number of components, i.e., rank(R) > n, and rank(R) = min(m, p). Thus, P-matrix analysis is associated with the problem of substituting R with an R that produces rank(R ) = n. This is mostly done by orthogonal decomposition methods, such as principal components analysis, partial least squares (PLS), or continuum regression [4]. Dimension requirements of involved matrices for these methods are m > n, and p > n. If the method of least squares is used, additional constraints on matrix dimensions are needed [4]. The approach of P-matrix analysis does not require quantitative concentration information of all constituents. Specifically, calibration samples with known concentrations of analytes under investigation satisfy the calibration needs. The method of PLS will be used in this chapter for P-matrix analysis. 

The ultimate development in the field of sample preparation is to eliminate it completely, that is, to make a chemical measurement directly without any sample pretreatment. This has been achieved with the application of chemometric near-infrared methods to direct analysis of pharmaceutical tablets and other pharmaceutical solids (74-77). Chemometrics is the use of mathematical and statistical correlation techniques to process instrumental data. Using these techniques, relatively raw analytical data can be converted to specific quantitative information. These methods have been most often used to treat near-infrared (NIR) data, but they can be applied to any instrumental measurement. Multiple linear regression or principal-component analysis is applied to direct absorbance spectra or to the mathematical derivatives of the spectra to define a calibration curve. These methods are considered secondary methods and must be calibrated using data from a primary method such as HPLC, and the calibration material must be manufactured using an equivalent process to the subject test material. However, once the calibration is done, it does not need to be repeated before each analysis. 

Methods Stored samples (both plasma and serum) from prior studies (1986-2008) in Ghana, Cameroon, Guatemala, Liberia, India, and the United States were used. Samples were analyzed, after protein precipitation, by LC-ESI-TOF. Specific analytes underwent additional studies using QTOF for MS/MS and FT-ICRMS for accurate mass measurement. Results were processed using principal component analysis (PCA) and machine learning algorithms. 

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