Principal component analysis, analytical

Chen, R, Ln, Y., Harrington, P.B. (2008) Biomarker profiling and reprodncibiUty stndy of MALDI-MS measurements of Escherichia coli by analysis of variance-principal component analysis. Analytical Chemistry, 80, 1474-1481. 

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... 

Probability that the analyte A is present in the test sample Conditional probability probability of an event B on the condition that another event A occurs Probability that the analyte A is present in the test sample if a test result T is positive Score matrix (of principal component analysis)... 

Multivariate analytical images may be processed additionally by chemo-metrical procedures, e.g., by exploratory data analysis, regression, classifica-tion> and principal component analysis (Geladi et al. [1992b]). 

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. 

A sample may be characterized by the determination of a number of different analytes. For example, a hydrocarbon mixture can be analysed by use of a series of UV absorption peaks. Alternatively, in a sediment sample a range of trace metals may be determined. Collectively, these data represent patterns characteristic of the samples, and similar samples will have similar patterns. Results may be compared by vectorial presentation of the variables, when the variables for similar samples will form clusters. Hence the term cluster analysis. Where only two variables are studied, clusters are readily recognized in a two-dimensional graphical presentation. For more complex systems with more variables, i.e. //, the clusters will be in -dimensional space. Principal component analysis (PCA) explores the interdependence of pairs of variables in order to reduce the number to certain principal components. A practical example could be drawn from the sediment analysis mentioned above. Trace metals are often attached to sediment particles by sorption on to the hydrous oxides of Al, Fe and Mn that are present. The Al content could be a principal component to which the other metal contents are related. Factor analysis is a more sophisticated form of principal component analysis. 

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). 

M.-L. O Connell, T. Howley, A.G. Ryder, M.N. Leger and M.G. Madden, Classification of a target analyte in solid mixtures using principal component analysis, support vector machines, and Raman spectroscopy, Proc. SPIE-Int. Soc. Opt. Eng., 5826, 340-350 (2005). 

The relative ease at which non-statisticians can make use of a sophisticated technique such as Principal Component Analysis speaks to its power in the hands of more accomplished practitioners or chemometricians. Simple univariate analyses are not sufficient to adequately check the large volume of data coming from state-of-the-art chemical analytical procedures. 

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. 

The rapid classification of polymeric species is an important problem in the area of analytical chemistry in general and of particular relevance to recycling and waste management. To accomplish classification tasks, a combination of spectral data and principal component analysis (PCA) is often employed. 

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. 

PCR creates a quantitative model in a two-step process (1) the so-called principal components analysis (PCA) scores (they are described just below), T, of the I calibration samples are calculated for A factors and then (2) the scores are regressed against the analyte concentration. 

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. 

Raman spectroscopy can also directly benefit TE analysis by non-invasively monitoring the growth and development of ECM by different cells on a multitude of scaffold materials exposed to various stimuli (e.g. growth factors, mechanical forces and/or oxygen pressures). Indeed the non-invasive nature of Raman spectroscopy enables the determination of the rate of ECM formation and the biochemical constituents of the ECM formed. Univariate (peak area, peak ratios, etc.) and multivariate analytical techniques (e.g. principal component analysis (PCA)) can be used to determine if there are any significant differences between the ECM formed on various scaffolds and/or cultured with different environmental parameters, and what these biochemical differences are. Least square (LS) modelling, for example, could allow the quantification of the relative components of the ECM formed (Fig. 18.3) [4, 38],... 

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