Principle Component Analyses

Fig. 9. Two-dimensional sketch of the 3N-dimensional configuration space of a protein. Shown are two Cartesian coordinates, xi and X2, as well as two conformational coordinates (ci and C2), which have been derived by principle component analysis of an ensemble ( cloud of dots) generated by a conventional MD simulation, which approximates the configurational space density p in this region of configurational space. The width of the two Gaussians describe the size of the fluctuations along the configurational coordinates and are given by the eigenvalues Ai.

On the other hand, techniques like Principle Component Analysis (PCA) or Partial Least Squares Regression (PLS) (see Section 9.4.6) are used for transforming the descriptor set into smaller sets with higher information density. The disadvantage of such methods is that the transformed descriptors may not be directly related to single physical effects or structural features, and the derived models are thus less interpretable. 

Yunker, M.B. and Cretney, W.J. (1996). Dioxins and furans in crab hepatopancreas uses of principle component analysis to classify congener patterns and determine linkages to contamination sources. In M. Servos, K.R. Munkittrick J H. Carey, and G.J. van der Kraak (Eds.) Environmental Fate and Effects of Pulp and Paper Mill Effluents. Delray Beach, FL St. Lucie Press, pp. 315-325. 

To further analyze the relationships within descriptor space we performed a principle component analysis of the whole data matrix. Descriptors have been normalized before the analysis to have a mean of 0 and standard deviation of 1. The first two principal components explain 78% of variance within the data. The resultant loadings, which characterize contributions of the original descriptors to these principal components, are shown on Fig. 5.8. On the plot we can see that PSA, Hhed and Uhba are indeed closely grouped together. Calculated octanol-water partition coefficient CLOGP is located in the opposite corner of the property space. This analysis also demonstrates that CLOGP and PSA are the two parameters with... 

Samola and Urleb [15] reported qualitative and quantitative analysis of OTC using near-infrared (NIR) spectroscopy. Multivariate calibration was performed on NIR spectral data using principle component analysis (PCA), PLS-1, and PCR. 

Since in many applications minor absorption changes have to be detected against strong, interfering background absorptions of the matrix, advanced chemometric data treatment, involving techniques such as wavelet analysis, principle component analysis (PCA), partial least square (PLS) methods and artificial neural networks (ANN), is a prerequisite. 

Figure 7.6 Principle components analysis (PCA) of PCB congener concentrations in technical Aroclor mixtures, contaminated water, caged brown trout, SPMDs, and hexane filled dialysis bags. The plot shows that 77% of the variance of samples within the 95% confidence ellipse is explained by PCI and PC2 and that caged fish and SPMDs are clustered together (PCA plot courtesy of Kathy Echols, USGS-CERC, Columbia, MO, USA).

Lipopolysaccharide extracts from different pathogenic and nonpatho-genic . coli strains were also analyzed by FT-IR with principle component analysis and canonical variate analysis (Kim et al, 2006b). The data showed that E. coli strains can be discriminated with >95% accuracy. Listeria species were also reliably classified by FT-IR coupled with an artificial neural network technology with a success rate of 96% (Rebuffo et al, 2006), while the identification rate for L. monocytogenes alone was 99.2%. 

Chemometric evaluation methods can be applied to the signal from a single sensor by feeding the whole data set into an evaluation program [133,135]. Both principle component analysis (PCA) and partial least square (PLS) models were used to evaluate the data. These are chemometric methods that may be used for extracting information from a multivariate data set (e.g., from sensor arrays) [135]. The PCA analysis shows that the MISiC-FET sensor differentiates very well between different lambda values in both lean gas mixtures (excess air) and rich gas mixtures (excess fuel). The MISiC-FET sensor is seen to behave as a linear lambda sensor [133]. It... 

Figure 9.9 Principle component analysis plot of PC2 vs. PC3 during the drying process of Ml wetcake by NIRS in-line monitoring. Reprinted with permission from Zhou etal. (2003).59...

Osanna, A., and Jacobsen, C. (2000). Principle component analysis for soft X-ray spectromicroscopy. In X-Ray Microscopy Proceedings of the Sixth International Conference, Meyer-Ilse, W., Warwick, T., and Attwood, D., eds., American Institute of Physics, Melville, New York, pp. 350-357. 

Barona, A. and Romero, F. (1996a) Distribution of metals in soils and relationships among fractions by principle component analysis. Soil Techtwl., 8, 303-319. 

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