Principal component analysis studies

N. Delaunay, V. Pichon and M.C. Hennion, Experimental comparison of three monoclonal antibodies for the class-selective immunoextraction of triazines. Correlation with molecular modeling and principal component analysis studies. J. Chromatogr.A 999 (2003) 3-15. 

Y. Wu, K. Murayama, Y. Ozaki. Two-Dimensional infrared spectroscopy and Principal Component Analysis studies of the secondary structure and kinetics of Hydrogen-Deuterium exchange of Human Serum Albumin. 7 FZtys Chem 105 6251-6259, 2001. 

The previously mentioned data set with a total of 115 compounds has already been studied by other statistical methods such as Principal Component Analysis (PCA), Linear Discriminant Analysis, and the Partial Least Squares (PLS) method [39]. Thus, the choice and selection of descriptors has already been accomplished. 

The field points must then be fitted to predict the activity. There are generally far more field points than known compound activities to be fitted. The least-squares algorithms used in QSAR studies do not function for such an underdetermined system. A partial least squares (PLS) algorithm is used for this type of fitting. This method starts with matrices of field data and activity data. These matrices are then used to derive two new matrices containing a description of the system and the residual noise in the data. Earlier studies used a similar technique, called principal component analysis (PCA). PLS is generally considered to be superior. 

A first introduction to principal components analysis (PCA) has been given in Chapter 17. Here, we present the method from a more general point of view, which encompasses several variants of PCA. Basically, all these variants have in common that they produce linear combinations of the original columns in a measurement table. These linear combinations represent a kind of abstract measurements or factors that are better descriptors for structure or pattern in the data than the original measurements [1]. The former are also referred to as latent variables [2], while the latter are called manifest variables. Often one finds that a few of these abstract measurements account for a large proportion of the variation in the data. In that case one can study structure and pattern in a reduced space which is possibly two- or three-dimensional. 

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. 

Forgacs, E. and Cserhati, T., Use of principal component analysis for studying the separation of pesticides on polyethylene-coated silica columns, J.Chro-matogr. A, 797, 33-39, 1998. 

In general, the evaluation of interlaboratory studies can be carried out in various ways (Danzer et al. [1991]). Apart from z-scores, multivariate data analysis (nonlinear mapping, principal component analysis) and information theory (see Sect. 9.2) have been applied. 

Different categories of Zonyl polymers are studied by ToF-SIMS both in the positive and negative ion mode. Studies have shown that, for each polymer, a specific fingerprint is obtained and the peaks corresponding to the specific chemical moieties of each polymer are detected (Figure 15.4). To represent this good selectivity, Principal Component Analysis is performed on the obtained spectra. The result clearly discriminates the different polymers. ToF-SIMS is then suited to the characterization of these materials. 

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. 

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. 

Methods Results The flow diagram (Fig. 2) outlines the methods used for the review and separation of the rocks present in the area. Image enhancement is done to increase the variance in the dataset. Contrast manipulation, spatial feature manipulation, and multi-image manipulation are used as digital enhancement techniques (Lillesand et al. 2007). In this study multi-image manipulation is used, which includes Band Ratio and Principal Component Analysis. 

Computational methods have been applied to determine the connections in systems that are not well-defined by canonical pathways. This is either done by semi-automated and/or curated literature causal modeling [1] or by statistical methods based on large-scale data from expression or proteomic studies (a mostly theoretical approach is given by reference [2] and a more applied approach is in reference [3]). Many methods, including clustering, Bayesian analysis and principal component analysis have been used to find relationships and "fingerprints" in gene expression data [4]. 

Principal component analysis can be further extended to study the chi-square statistic, since... 

In a rare example which demonstrates the possibilities of the approach Biirgi and Dubler-Steudler (1988a) have recently combined structure and reactivity data in a detailed study of the ring-inversion reaction of a homogeneous set of organometallic compounds. The reaction is the auto-merization of zircocene and hafnocene complexes [73 M = Zr or Hf, X = C or O], known from temperature-dependent NMR measurements to undergo the equilibration [73]—s.[73 ]. Principal-component analysis of... 

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). 

Price, A.L., Patterson, N.J., Plenge, R.M., Weinblatt, M.E., Shadick, N.A., and Reich, D. (2006) Principal components analysis corrects for stratification in genome-wide association studies. Nat. Genet. 38, 904-909. Available at http //genepath.med.Harvard.edu/ reich/ EIGENSTRAT.htm. 

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

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