Principal component analysis INDEX

Musumarra et al. [44] also identified miconazole and other drugs by principal components analysis of standardized thin-layer chromatographic data in four eluent systems and of retention indexes on SE 30. The principal component analysis of standardized R values in four eluents systems ethylacetate-methanol-30% ammonia (85 10 15), cyclohexane-toluene-diethylamine (65 25 10), ethylacetate-chloroform (50 50), and acetone with plates dipped in potassium hydroxide solution, and of gas chromatographic retention indexes in SE 30 for 277 compounds provided a two principal components model that explains 82% of the total variance. The scores plot allowed identification of unknowns or restriction of the range of inquiry to very few candidates. Comparison of these candidates with those selected from another principal components model derived from thin-layer chromatographic data only allowed identification of the drug in all the examined cases. 

Fig. 3. Coverage of chemistry space by four overlapping sublibraries. (A) Different diversity libraries cover similar chemistry space but show little overlap. This shows three libraries chosen using different dissimilarity measures to act as different representations of the available chemistry space. The compounds from these libraries are presented in this representation by first calculating the intermolecular similarity of each of the compounds to all of the other compounds using fingerprint descriptors and the Tanimoto similarity index. Principal component analysis was then conducted on the similarity matrix to reduce it to a series of principal components that allow the chemistry space to be presented in three dimensions.

The McReynolds data were standardized and subjected to principal component analysis by several groups of workers who were able to reduce the data to three statistical components. Burns and Hawkes42 further refined the calculations to produce four quasi-theoretical indices that measure dispersion, polarity, acidity, and basicity. Hawkes has described this process in a more recent paper43 in which his group confirmed and refined these calculations with spectroscopic measurements. In addition to justifying their approach, they provide four indices for each of the 26 common liquid phases that were identified earlier as being the most important.36 The dispersion index is calculated from refractive indices, but the other three indices are based at least partially on chromatographic data. 

Using a different set of standard substances, i.e. substituting 1-butanol, pentan-2-one, and 1-nitropropane for the rather volatile ethanol, butan-2-one, and nitromethane, McReynolds developed an analogous approach [103]. Altogether, he characterized over 200 liquid stationary phases using a total of 10 probes. A statistical analysis of the McReynolds retention index matrix using the principal component analysis method has shown that only three components are necessary to reproduce the experimental data matrix [262]. The first component is related to the polarity of the liquid phase, the second depends almost solely on the solute, and the third is related to specific interactions with solute hydroxy groups [262]. 

IlMei et al. (39) derived the VHSE5 composite index of electronic effects. This scale (Vectors of Hydrophobic, Steric, and Electronic properties) was derived from principal components analysis of 50 different physico-chemical variables. 

The Z3 electronic index was taken from Hellberg et al. (25). This scale was derived from principal components analysis of 29 variables. The Z3 index was completely independent from hydrophobic (zl scale) and steric (z2 scale) effects. 

Because almost all materials used in the pharmaceutical industry have NIR spectra, the use of NIR for assuring blend homogeneity may prove to be a valuable application. Ciurczak [24,25] reported some of the first work on this subject. His work involved the use of a fiber probe to collect spectra from various locations in the mixer. Spectral matching and principal component analysis (PCA) were used to measure how similar the powder mix in a particular portion of the blender was to a predetermined good, or complete, mix. The match index or PCA scores were plotted versus time to assess the optimal blending time. 

Based on the Principal Component Analysis, the LIN index (leaching index) and the VIN index (volatility index) were defined in terms of the first and second PCs, respectively, explaining 92.7% of the total variance [Gramatica and Di Guardo, 2002]. PCs were calculated on a data set of 135 pesticides, described by vapour pressure (Vp), Henry s law constant (H), water solubility (Sw), and octanol/water (Kqw) and organic carbon (Kqc) partition coefficients. The LIN and VIN indices are defined as the following ... 

The Global Leachability Index (GLI index) [Papa, Castiglioni et al, 2004] was defined by Principal Component Analysis, condensing information derived from GUS index, modified LEACH index, and LIN index. 

The literature of QSRR with LSS is dominated by a specific SSD, the I ER solute parameters V, E, S, A, and B, as defined in Equation 15.2. An extraordinary amount of attention has been paid to predict retention (24,25) and to establish phase selectivity in MEKC using LSER (5, 7, 26-31). Attempts to classify and to contrast micellar phases with basis on the LSER coefficients have been pursued by many researchers (5,26,27,29). Interesting approaches comprise the classification of micellar phases by the combined use of LSER parameters and retention indexes (32), the clustering of micellar systems by principal component analysis (26), the use of LSER parameters to compose vectors for characterization of lipophilicity scales (33), and, more recently, the establishment of micellar selectivity triangles (34,35) in analogy to the solvent selectivity triangle introduced by Snyder to classify solvents and ultimately mobile phases in liquid chromatography. 

Another recommendation was to examine the correlation matrix of the covariates prior to the analysis and determine whether any two covariates were correlated. If any two correlated covariates were found to be important predictor variables, one could possibly transform the variables into a composite variable, such as the transformation of height and weight into body surface area or body mass index, or to use only the covariate with the greatest predictive value in the model and not to include the other covariate. An untested approach would be to use principal component analysis and then use one or more of the principal components as the covariate in a model. 

Figure 9.15 Scatter plots of the first three principal components of all structural parameters and variance components. Each index patient was singularly removed from the data set and the model in Eq. (9.14) was refit using FOCE-I. The resulting matrix of structural parameters and variance components was then analyzed using principal components analysis. Influential observations are noted in the figures. Patient 100, who had a BSA of 2.52m2 and a BMI of 31.2kg/m2, is denoted as a solid square.

Seven parameters of physicochemical properties, such as acid number, color, density, refractive index, moisture and volatility, saponification value and PV, were measured for quality and adnlter-ated soybean, as well as quality and rancid rapeseed oils. The chemometric methods were then applied for qualitative and quantitative discrimination and prediction of the oils by methods snch as exploratory principal component analysis (PCA), partial least squares (PLS), radial basis function-artificial neural networks (RBF-ANN), and multi-criteria decision making methods (MCDM), PROMETHEE and GAIA.260... 

First of all, an observation matrix was established. Suppose that there were n samples and p variables for each sample. Then the data matrix of n x p order was formed. Next, the indexes were standardized. Because the dimension, size and evaluation index of each factor in the principal component analysis had large difference, the comparability was poor. In order to eliminate the difference in dimension and order of magnitudes and to obtain the comparability between the indexes, the original data should be standardized first. Then the indexes were homogenized. The reciprocal was taken for the reverse index. 

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