Component score

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.

Table 5. Linear regression between principal component scores antibiotic resistance MPNs and soil physico-chemical characteristics based on the...

Fig. 2. Plots of 2nd principal component scores (x-axis) verses 3rd principal component scores (y-axis) showing the regions of space where unknown spessartine data points would be classified as originating from one of the four geographic locations Brazil, Virginia, Australia, and China, clockwise form upper right, respectfully.

More definitive information may also be gleaned from PCA. In Fig. 6.9, three principal component scores are graphed to show how the amount of roasting in coffee beans may be ascertained. 

Classification To illustrate the use of SIMCA in classification problems, we applied the method to the data for 23 samples of Aroclors and their mixtures (samples 1-23 in Appendix I). In this example, the Aroclor content of the three samples of transformer oil was unknown. Samples 1-4, 5-8, 9-12 and 13-16, were Aroclors 1242, 1248, 1254, and 1260, respectively. Samples 17-20 were 1 1 1 1 mixtures of the Aroclors. Application of SIMCA to these data generated a principal components score plot (Figure 12) that shows the transformer oil is similar, but not... 

An examination of the sample distributions observed in principal components projections using isomer concentration data expressed as fractional composition, as well as the clustering of samples by similar values of their second principal component score term, revealed consistent differences existed in sample profiles. The next step in this data evaluation is to statistically analyze correlations of the PLS components from analyses with the external variables such as percent sand, clay and silt, and total organic matter in samples. These correlations may play an important role in identifying factors resulting in changes in PCB composition and enable one to more clearly understand the forces determining the distribution and fate of PCB in a complex ecosystem. 

Figure 3. 3-D Plot of Principal Components Scores (Theta-1,-2,-3) Representing Normalized Isomer Composition Data for Aroclors 1242, 1248, 1254, 1260, and their mixtures. The points for each Aroclor represent individual sample analyses. The plot in the upper right quadrant is the view parallel to the Z-axis.

We thank Michael Koehler (University of Illinois at Chicago) for developing the combined two- and three-dimensional plotting program to display the sample component scores. 

There are four component scores that can be used to assess how informative and desirable a compound might be. These scores are as follows ... 

Once all of the component scores are defined and calculated, one can then compute the Q-score by forming a linear combination of the components. For example, Q-score could be computed using the formula shown in Eq. 2.5 ... 

The goal of the prioritization scheme is to design the scores so that the overall worst looking compounds are de-emphasized and the best looking compounds are moved toward the top of the list. Thus, it is important to ensure that the best and the worst compounds are clearly separated and that the vast bulk of the population is in the middle. The normal distribution is ideally suited for this and thus it is advantageous to transform our component scores into a normal-like distribution. Enterprise Miner from SAS Institute was used to do this as it has a maximize normality transformation built into it. 

Compute the normalized and regularized component scores (B-score and Q-score)... 

Figure 4.70. Principal component score plot of ail samples in class B (after remov-i si=i-=--ing the mislabeled samples). The samples in the calibration set are Xs and the vali- dation samples are Os. 

Figure 1.26. Example of a component score for a single descriptor (molecular weight, MW adapted from Lajiness and Shanmugasundaram 2004)...

After regularization of the component scores, the following consensus score (CS) was calculated ... 

Figure 7.2 Principal component scores plot for a set of dopamine mimetics. Compounds with teratogenic activity are indicated by filled circles. (From Ridings, J.E., Manallack, D.T., Saunders, M.R., Baldwin, J.A., and Livingstone, D.J., Toxicology, 76, 209-217, 1992. With permission.)...

Regression on principal components (PCR) is another from of regression modeling that may be used for continuous response data. Here, the independent variables (the x set) are computed from the descriptor variables using PC A as shown in Equation 7.1. These are the principal component scores and they have several advantages ... 

With PCA, it is possible to build an empirical mathematical model of the data as described by Equation 4.4 where Tk is the n x k matrix of principal component scores and k is the m x A matrix of eigenvectors. 

As the first pure component begins to elute, the principal component scores increase in Figure 4.15 along the axis labeled pure component 1. As the second component begins to elute, the points shift way from the component 1 axis and toward the component 2 axis. As the concentration of the second component begins to decrease, the principal component scores decrease along the axis labeled pure component 2. Points that lie between the two pure-component... 

FIGURE 4.15 Scatter plot of the principal component scores from the analysis of the HPLC-UV/visible data set shown in Figure 4.1. The principal component axes are orthogonal, whereas the pure-component axes are not. Distances from the origin along the pure-component axes are proportional to concentration. Pure spectra lie on the pure-component axes. Mixture spectra he between the two pure-component axes. Dashed lines show the coordinates (e.g., concentrations) of one point on the pure-component axes. 

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