PLS score plots

Fig. 17.2. PLS score plot for the VolSurf Caco-2 model. Light open circles represent penetrating compounds dark open circles represent nonpenetrating compounds. Filled circles represent the projection (prediction) of compounds in Table 17.1 in the Caco-2 model.

FIGURE 5.98. Factor 2 versus Factor 1 PLS scores plot for component A. 

Figure 4.10. PLS score plot separating the stable compounds (red circles) fron unstable compounds (blue circles). Prediction (white circles) oftheyesorno response for a set of 265 stable BioPrint compounds.

Figure 8.5. The 2D PLS scores plot of the VDVolSurf library model (open grey points) as well as the projection of the predictions for the ten test set compounds (filled points) are shown. The middle bar represents the best discrimination between training set compounds (with high and low VD).

Figure 8.6. Proiection of 1346 compounds from Johnson, Johnson on the 2D PLS scores plot of the VolSurf metabolic stability model (open grey points). The black line discriminates between unstable and stable compounds in the metabolic stability model projected compounds on the left of the black line are predicted as unstable (%MS < 40), while...

Fig. 7.6. A PLS scores plot for a set of halogenated ether anaesthetics the ellipses enclose compounds with similar side-effects (from Hellberg et a/. 1985, with permission of VCH,...

To view the relationships between the compounds, consider the PLS score plot in Figure 5. (Figure 6 accounts for a minor portion of the Y variance, and is neglected for this reason.) This graph summarizes well the distribution of the nitrobenzene derivatives along the various toxicity... 

The VolSurf method was used to produce molecular descriptors, and PLS discriminant analysis (DA) was applied. The statistical model showed two significant latent variables after cross-validation. The 2D PLS score model offers a discrimination between the permeable and less permeable compounds. When the spectrum color is active (Fig. 17.2), red points refer to high permeability, whereas blue points indicate low permeability. There is a region in the central part of the plot with both red and blue compounds. In this region, and in between the two continuous lines, the permeability prediction is less reliable. The permeability model... 

The described projection method with scores and loadings holds for all linear methods, such as PCA, LDA, and PLS. These methods are capable to compress many variables to a few ones and allow an insight into the data structure by two-dimensional scatter plots. Additional score plots (and corresponding loading plots) provide views from different, often orthogonal, directions. 

Scores Plot (Sa nple Diagnostic) The score plots show the relationship of the samples in LS row space and are examined for consistency with what is known about dse data set. Look for unusual or inconsistent patterns which can indicate potential problems with the model and/or samples (see also PCA, Section 4.2.2). 1b the PCA discussion the scores are referred to as PCs, but in PLS they are referred to as factors. 

With the molecular descriptors as the X-block, and the senso scores for sweet as the Y-block, PLS was used to calculate a predictive model using the Unscrambler program version 3.1 (CAMO A/S, Jarleveien 4, N-7041 Trondheim, Norway). When the full set of 17 phenols was us, optimal prediction of sweet odour was shown with 1 factor. Loadings of variables and scores of compounds on the first two factors are shown in Fig es 1 and 2 respectively. Figure 3 shows predicted sweet odour score plotted against that provid by the sensory panel. Vanillin, with a sensory score of 3.3, was an obvious outlier in this set, and so the model was recalculated without it. Again 1 factor was r uired for optimal prediction, shown in Figure 4. 

Figure 3. Sweet score predicted by PLS model plotted against measured sensory score for 17 volatUe phenols.

Figure 4.13 Preliminary PLS model developed to seek out outlying samples using the scores plots. The scores of the most important factor (tl) are always plotted on the abscissa. Sample 4 has a different behaviour because the tail of the atomic peak had a strange elevation and this was detected on the third factor. Note that the samples show some grouping because of the experimental design used to prepare the calibration set.

FIGURE 4.2 PLS-DA score plot performed on the H NMR spectra of wines. The plot shows the clear discrimination among Australian Shiraz wines (square) and French (circle), Californian (triangle), and Australian (star) Cabernet Sauvignon wines. 

While PCA can reveal structure in a set of data viewed in isolation, PLS can be used to disclose structure in the data in view of external information [19-21]. The amphetamine example was analysed by PCA above without using the knowledge about the treatment that each subject received. In PLS, such information can be included. This corresponds to tilting the PC so that the score vector better describes the relation between the treatment and the changes in the measured responses. In Figures 6.12 and 6.17, the PLS scores of the BHT data and the amphetamine data are plotted, respectively. The strategy used in PLS is to add a new matrix, Y, in addition to the matrix of measurements X. The matrix Y contains external information such as treatment of each... 

PLS has been used mainly for calibration purposes in analytical chemistry. In this case the determination of unknown concentrations is the most important demand. In spectroscopic research, there is also the interpretation of diagnostic plots such as the score plots and loading plots as a function of reaction mechanisms and spectroscopic background knowledge. Also the interpretation of rank as complexity of a mechanism is a valuable tool. A nice property of latent variable methods is that they do not demand advanced knowledge of the system studied, but that the measurements... 

In the preceding description of the Mahalanobis distance, the number of coordinates in the distance metric is equal to the number of spectral frequencies. As discussed earlier in the section on principal component analysis, the intensities at many frequencies are dependent, and by using the full spectrum, we fit the noise in addition to the real information. In recent years, Mahalanobis distance has been defined with PCA or PLS scores instead of the spectral frequencies because these techniques eliminate or at least reduce most of the overfitting problem. The overall application of the Mahalanobis distance metric is the same except that the rt intensity values are replaced by the scores from PCA or PLS. An example of a Mahalanobis distance calculation on a set of Raman spectra for 25 carbohydrates is shown in Fig. 5-11. The 25 spectra were first subjected to PCA, and it was found that the first three principal components could account for most of the variance in the spectra. It was first assumed that all 25 spectra belonged to the same class because they were all carbohydrates. However, as shown in the three-dimensional plot in Fig. 5-11, the spectra can be clearly divided into three separate classes, with two of the spectra almost equal distance from each of the three classes. Most of the components in the upper left class in the two-dimensional plot were sugars however, some sugars were found in the other two classes. For unknowns, scores have to be calculated from the principal components and processed in the same way as the spectral intensities. 

A very useful method of discriminating between samples from different classes is to plot PCA or PLS scores in two or three dimensions. This is very similar to the Mahalanobis distance discussed earlier in Fig. 5-11, except that it is limited to two or three dimensions, and the Mahalanobis distance can be constructed for n dimensions. Score plots do provide a good visual understanding of the underlying differences between data from samples belonging to different classes. 

The impact of shape was reduced, whereas the impact of the Water, Dry and Mix was reinforced. Then the data were correlated to the activity by means of PLS analysis. The PLS method condensed the overall information into two smaller matrices, which can be visualized by means of the score plot (which shows the pattern of the compounds) and the loading plot (which shows the pattern of the descriptors). The optimal model was obtained with three components, exhibiting a significant statistical quality, as evinced by good R = 0.94 and = 0.71 values. 

Figure 10.7. Score plot from a PLS analysis, (a) Caco-2 cell monolayer (b) blood-brain barrier. Compounds that pass the barrier by a passive mechanism are shown in gray, and those that do not are shown in black. PLS coefficients (c) Caco-2 cell monolayer (d) blood-brain barrier.

A plot of the score vectors against each other, e.g. against tj, shows the positions of the projected object points in the plane spanned by the PLS vectors in ths X space, and a plot of U2 against Uj shows the same for the Y space. These plots are therefore similar to the score plots from principal components analysis. 

FIGURE 10.9 (a) Representative reversed-phase UPLC-Q-TOF MS TICs of a urine sample analyzed in positive and negative ion modes (b) PLS-DA scores plot (OSC filtered) of healthy, insulin-sensitive subjects (A) and prediabetic, insulin-resistant individuals ( ) (c) corresponding PLS-DA loading plot. The variables are labeled with m/z, and m/z 194.34 is labeled by an arrow and (d) differences in the TIC peak height of m/z between insulin-sensitive subjects (A) and insulin-resistant individuals ( ). p < 0.05 vs. insulin-resistant individuals analyzed by the Wilcoxon rank sum test. (Reprinted from Chen, J. et al., Anal. Chem., 80, 1280, 2008. With permission.)... 

Principal component analysis and partial least squares analysis are chemometric tools for extracting and rationalizing the information from any multivariate description of a biological system. Complexity reduction and data simplification are two of the most important features of such tools. PCA and PLS condense the overall information into two smaller matrices, namely the score plot (which shows the pattern of compounds) and the loading plot (which shows the pattern of descriptors). Because the chemical interpretation of score and loading plots is simple and straightforward, PCA and PLS are usually preferred to other nonlinear methods, especially when the noise is relatively high. ... 

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