Principal component based plots

Scores and loadings plots of PC2 versus PCI of the raw data in Table 6.1 

A useful trick is to normalise tire scores. This involves calculating 

Note that there is often confusing and conflicting terminology in the literature, some authors called this summing to a constant total normalisation, but we will adopt only one convention in this book however, if you read the original literature be very careful 

Three-dimensional projections of scores (top) and loadings (bottom) for dataset A 

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Fig. 3. Principal component score plots based on the antibiotic resistance profiles. The diamond ( ), the open square (o) and the triangle (A) indicate BG, DDF and DEF, respectively. The value in the parenthesis indicates the percentage of the variability explained by the principal component.

While the deuterium spectra of benzaldehydes from different sources do not appear (upon visual inspection) to have significant differences from one another, other than some variation in intensity, the deuterium distribution of benzaldehyde does form clusters on a principal component analysis plot. Benzaldehyde products from the same source have similar deuterium distributions and are therefore close to each otlier on the plot (Figure 1). Thus, the origin of benzaldehyde can be differentiated based on site-specific deuterium distribution. Products outside of the clusters of knoivn samples are normally considered as originating from an unknown source or as a mixture of benzaldehyde from different known sources. 

Figure 13.3-4. Principal components scores plots (PCI vs. PC2) based on 600-MHz H NMR spectra of rat nrine. (a) Standard trajectory analysis of urinary NMR data obtained after treatment with hydrazine from identical studies repeated at different sites, open and closed symbols, (b) The same data after application of the trajectory matching technique, SMART. Error bars represent the standard error for each time point average [28].

Figure 2.11 Plot of compounds developed for different target classes based on a principal components analysis (PCA) of 2D structure-based property fingerprints. Compounds are coded according to their target class (triangle, PDE square, 5HT receptor diamond, statin circle, F-quinoline antibiotics) and clinical status at the time (gray, ok yellow, clearance issue red,...

Pattern recognition studies on complex data from capillary gas chromatographic analyses were conducted with a series of microcomputer programs based on principal components (SIMCA-3B). Principal components sample score plots provide a means to assess sample similarity. The behavior of analytes in samples can be evaluated from variable loading plots derived from principal components calculations. A complex data set was derived from isomer specific polychlorinated biphenyl (PCBS) analyses of samples from laboratory and field studies. 

These applications demonstrate that pattern recognition techniques based on principal components may be effectively used to character zate complex environmental residues. In comparisons of PCBs in bird eggs collected from different regions, we demonstrated through the use of SIHCA that the profiles in samples from a relatively clean area differed in concentration and composition from profiles in samples from a more highly contaminated region. Quality control can be evaluated by the proximity of replicate analysis of samples in principal components plots. 

Principal Component Analysis (PCA) is performed on a human monitoring data base to assess its ability to identify relationships between variables and to assess the overall quality of the data. The analysis uncovers two unusual events that led to further investigation of the data. One, unusually high levels of chlordane related compounds were observed at one specific collection site. Two, a programming error is uncovered. Both events had gone unnoticed after conventional univariate statistical techniques were applied. These results Illustrate the usefulness of PCA in the reduction of multi-dimensioned data bases to allow for the visual inspection of data in a two dimensional plot. 

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. 

There are many advantages in using this approach to feature selection. First, chance classification is not a serious problem because the bulk of the variance or information content of the feature subset selected is about the classification problem of interest. Second, features that contain discriminatory information about a particular classification problem are usually correlated, which is why feature selection methods using principal component analysis or other variance-based methods are generally preferred. Third, the principal component plot... 

Figure 3. Principal components plot (components Nos. 1 and 2) based on the entire data set used for illustration.

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