Principal components plots

Figure 8.16 shows a principal component plot of that data the classification of which by MVDA was given in Fig. 8.11. It can be seen that a certain structure can be imagined which becomes clearer by the discrimination algorithm.

Fig. 8.16. Representation of a principal component plot (pi vs pi) of 88 German wines, see Fig. 8.11 and Thiel et al. [2004] o Bad Diirkheim (Rhinelande-Palatinate)...

Generate principal components plots of data blocks... 

One can use principal components plots to visually inspect higher dimensional data. Their use is equivalent to projecting the higher dimensional data onto a two-dimensional plane. Such plots are helpful in interpreting chromatographic or other scientific data composed of many measurements (peaks or dimensions). 

In the principal components plots presented in this paper, the number plotted corresponds to the sample identification number given in the appendix. If more than one sample has the same locus in the score (Theta s) or loading plots (Beta s), the letter M is plotted. The values for the sample coordinates in the principal components plots can be listed by the SIMCA-3B program. 

Figure Principal Components Plot Derived from Fractional Composition Replicate Aroclor Analysis (Figure 2).

Figure 10. Principal Components Plot (Theta 1 vs. Theta 2) from Aroclor Classes (Table IX).

Figure 12. Principal Components Plot from Five Aroclors Classes and a Used Transformer Fluid (most similar to Aroclor 1260).

Fig. 5.3 Principal component plots in pharmacophoric and topological spaces. Rectangles schematically indicate the activity zones .

T.J. Thurston, R.G. Brererton, D.J. Foord, R.E.A. Escott, Principal components plots for exploratory investigation of reactions using ultraviolet-visible spectroscopy application to the formation of benzophenone phenylhydrazone, Talanta, 63, 757-769 (2004). 

Figure 2. Principal Components Plots for Aroclor Samples (ref. Table I for Sample i.d.)...

Figure 5. Principal Components Plot Derived from Analysis of Aroclor Standards, Their Equal Mixture, and Eggs of Forster s Tern.

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. 

Figure 2. Principal component plot of x-ray data by laboratory.

Figure 4, Principal component plot of GC/MS data by sample.

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... 

Fig. 2. A plot of the two largest principal components developed from all of the features in the dataset does not show class separation. When principal components are developed from the features that contain information about the classes, sample clustering on the basis of class is evident in a principal component plot of the data.

The fitness function of the pattern recognition GA scores the principal component plots and thereby identifies a set of features that optimize the separation of the classes in a plot of the two or three largest principal components of the data. To facilitate the tracking and scoring of the principal component plots, class and sample weights, which are an integral part of the fitness function, are computed ... 

A prediction set of 19 compounds (see Table 2) was used to assess the predictive ability of the 15 molecular descriptors identified by the pattern recognition GA. We chose to map the 19 compounds directly onto the principal component plot defined by the 312 compounds and 15 descriptors. Figure 5 shows the prediction set samples projected onto the principal component map. Each projected compound lies in a region of the map with compounds that bare the same class label. Evidently, the pattern-recognition GA can identify molecular descriptors that are correlated to musk odor quality. 

Fig. 5. A plot of the two largest principal components of the training set developed from the 312 compounds and 15 molecular descriptors identified by the pattern-recognition GA. The plane defined by the two largest principal components accounts for 35% of the total cumulative variance. Circles are the musks inverted triangles are the nonmusks M = musks from the prediction set projected onto the principal component plot N = nonmusks from the prediction set projected onto the principal component plot.

Figure 3. Principal components plot (PC 2 vs. PC 4) demonstrating elements that drive variance in Jiskairumoko ochre...

The principal component plot of the objects allows a visual cluster analysis. The distances between data points in the projection, however, may differ considerably from the actual distance values. This will be the case when variances of the third and following principal components cannot be left out of consideration. A serious interpretation should include the application of at least another cluster analysis method (ref. 11,12). 

Table 3.4 shows the loadings of the first, second and third principal component the others have very small variances. In the principal component plots in Figure 3.9 the samples are represented by different symbols related to the average temperature during the sampling time. The scores computed for the first principal component clearly distinguish the cold and warm season. 

Fig. 3.9 Principal component plots of PAH data. Each point corresponds to an air sample.

To better understand the problems involved with classifying gas chromatograms of Jet-A and JP-5 fuels, it was necessary to focus attention on these two fuels. Figure 9.13 shows a plot of the two largest principal components of the 85 GC peaks obtained from the 110 Jet-A and JP-5 gas chromatograms. An examination of the principal component plot revealed that Jet-A and JP-5 fuel samples lie in different regions of the principal component map. However, the data points... 

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

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