Partition principal component analysis

Tip 5 Principal components analysis (PCA) the name of a statistical procedure Partitioning was based on principal components analysis. 

Key Words Biological activity chemical features chemical space cluster analysis compound databases dimension reduction molecular descriptors molecule classification partitioning algorithms partitioning in low-dimensional spaces principal component analysis visualization. 

Chemometrics can also be used to overcome some of the intrinsic deficiencies of sequential extraction, such as non-specificity. Barona and Romero (1996a) used principal components analysis (PCA) to establish relationships between the amounts of metals released at each stage of a sequential extraction procedure and bulk soil properties, and demonstrated that carbonates played a dominant role in governing metal partitioning in the soil studied. The same workers employed multiple regression analysis to study soil remediation (see Section 10.11.1.1). Zufiaurre et al. (1998) also used PCA to confirm their interpretation of phase association and hence potential bioavailability of heavy metals in sewage sludge. 

Vertically, the table shows the between-compound variation of the descriptors. Horizontally, the table shows the within-compound variations of the descriptors. Factor analysis and Principal Components Analysis partition these variations into... 

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 ... 

Performing principal component analysis on the ranks can help to assess the dimensionality of the ordering context. Since the marginal distributions of the ranks are the same except for ties, the difference between covariance matrix and correlation matrix is not critical. If there are subsets of indicators that segregate strongly in their loadings, then complexity is confirmed and it may be prudent to consider partitioning of the prioritization process. 

Several hundreds of linear relationships between various kinds of (mostly nonspecific) biological data and n-octanol/water partition coefficients have been published e.g. [18, 182]). However, the choice of n-octanol/water as the standard system for drug partitioning must be reconsidered in the light of some recent results. Principal component analysis of partition coefficients from different solvent systems [188 —190] shows that lipophilicity depends on solute bulk, polar, and hydrogen-bonding effects [189] isotropic surface areas, i.e. areas where no water molecules bind and hydrated surface areas, were correlated with the first and the second principal components of such an analysis [190]. 

Dunn III, W. J., Grigoras, S. and Johansson, E. (1986) Principal component analysis of partition coefficient data an approach to a new method of partition coefficient estimation, in Partition Coefficient Determination and Estimation (eds W. J. Dunn III, J. H. Block, R. S. Pearlman), Pergamon Press, New York, NY. 

The hydrophobic indices, i., the ratios of hydrophobic to hydrophilic surface areas, of seven monosaccharides have been determined. They were found to correlate well with the partition coefficients of the polystyrene-water system for monosaccharides. The concept of hydrophobic indices is important in the consideration of the hydrophobic interactions of flat molecules in aqueous solution. In an effort to establish quantitative structure-activity relationships for carbohydrates, an experimental data-matrix containing the values of sixteen monosaccharides in thirteen solvent systems was subjected to principal component analysis (PCA). Four PC s (t -t ) were found... 

An interesting approach proposed by Dunn et al. 4 is derived from a principal components analysis of partition coefficients measured in different organic solvents (M-octanol, diethyl ether, chloroform, benzene, carbon tetrachloride, hexane). Two principal components were selected. An analysis of the loadings matrix showed that the first component (f, 80% of the variance) is approximately equally weighted in the log P data in all solvents, whereas the... 

Fig. 1. Pattern recognition methods. ANN, artificial neural networks BP ANN, back-propagation ANN CA, cluster analysis CART, classification and regression trees (recursive partitioning) CCA, canonical correlation analysis CVA, canonical variate analysis kNN, -nearest neighbor methods LDA, linear discriminant analysis PCA, principal component analysis PLS DA, partial least squares regression discriminant analysis SIMCA, soft independent modeling of class analogy SOM, self-organizing maps.

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