PLS scores

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... 

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.

We now have enough information to find our PLS Scores matrix and PLS Loadings matrix. First of all the PLS Loadings matrix is simply the right singular values matrix or the V matrix this matrix is referred to as the P matrix in principal components analysis and partial least squares terminology. The PLS Scores matrix is calculated as... 

The data matrix A x the PLS Loadings matrix V = PLS Scores matrix T (23-3)... 

A partial least square type two (PLS 2) analysis was employed, based on a library of the three API pure components. Applying the model in classification mode to the sample data set results in PLS score images that show the spatial distribution of the three API components. 

The PLS scores images for acetaminophen, aspirin and caffeine highlighting high concentration areas for each chemical components are shown in Figure 8.11A-C. Contrast in these score images is based on the... 

Figure 8.11 An OTC analgesic tablet (Excedrin) with three APIs. Spatial distribution of each API was obtained using PLS analysis. (A-C) PLS score images of acetaminophen, aspirin, and caffeine, respectively and (D-F) single-pixel microspectra (solid line) compared to pure component acetaminophen, aspirin, and caffeine spectra (dashed line), respectively.

Figure 8.12 Histograms of PLS score images. (A) acetaminophen (B) aspirin and (C) caffeine.

Figure 8.15 (A-F) hiistogram representations of the PLS score images showing the statistical distributions of the API class. Heterogeneity In the blend Is Indicated by deviations from a normal distribution and can be expressed as percent standard deviation (%SD), calculated by dividing the standard deviation by the mean.

For the blend uniformity application, the primary concern is overall heterogeneity within the sample. This is directly indicated by the width of the distribution and is quantitatively measured as the percent standard deviation relative to the mean (%SD). The %SD value obtained from the PLS scores distribution from each of the six imaged tablets is noted on the histograms in Figure 8.15(A-F). The value of %STD consistently decreases as the blending quality of the sample improves. 

Figure 8.16 Analysis of selected areas of the best laboratory blend (Tablet E) and the commercial blend (tablet F). (a) Truncated PLS score imaged for the API component (depicted as white) from the central region of the tablets showing that on a local scale, the blending in both samples is uniform and (b) histograms and resulting %SD of the distribution from the truncated images. Note that both examples display nearly normal distributions.

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

The PLS scores are interpreted in the same way as PCA scores since they are the sample coordinates along the model components. The additional feature in PLS is that two different sets of components are considered, summarizing variations in the X space or Y space. PLS loadings express the relatedness of each X and Y variable to the model component. T scores are the coordinates of data points located in the X space that describe the part of structure in X which is most predictive for... 

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