We now present an example of the INDSCAL method applied to data collected on sulfathiazole using PXRD and Raman spectroscopy (Barr, Cunningham et al., 2009). A flowchart is shown in Fig. 3.8.15. Three polymorphs of sulfathiazole were prepared and PXRD data were collected on a Bruker C2 GADDS system. Each sample was run for 2 min over a 3–30° range in 2θ using Cu Kα radiation. Raman data were collected on a Bruker SENTINEL. The Raman probe was integrated into the PXRD instrument.

Figure 3.8.15 | top | pdf | A flowchart for the INDSCAL method using Raman and PXRD data. Note that any combination of any 1D data can be used here.

The only data pre-processing performed was background removal. Fig. 3.8.16(a) shows the resulting dendrogram (with the default cut level) and Fig. 3.8.16(b) shows the corresponding MMDS plot. To identify each sample they are numbered via a four-digit code: the first two digits are the well number, and the last digit defines whether the sample is form 2, 3 or 4 of sulfathiazole. It can be seen that the clustering is only partly successful: form 4 (red) is correctly clustered; form 3 (orange) gives five clusters and form 2 gives three clusters.

Figure 3.8.16 | top | pdf | Clustering 48 PXRD spectra with background corrections applied for three polymorphs of sulfathiazole. (a) The dendrogram. Each sample is identified by a four-digit code. The first two digits are the well number, and the last digit defines whether the sample is form 2, 3 or 4 of sulfathiazole. (b) The MMDS plot: the red cluster is well defined but the rest of the spheres are diffuse and intermingled. (c) The dendrogram derived from clustering 48 Raman spectra of sulfathiazole with background corrections applied. (d) The corresponding MMDS plot. The clusters are poorly defined. (e) The results of the INDSCAL method. The dendrogram is shown with the default cut level. The clustering is correct; all the samples are placed in the correct group except for patterns 35-2 and 45-2. (f) The MMDS plot validates the dendrogram. (g) The Raman patterns for 35-2 and 45-2 superimposed. They are primarily background noise.

Fig. 3.8.16(c) shows the clustering from the Raman spectra. The results are poor: most of form 2 is correctly clustered, but forms 4 and 3 are intermixed, and the MMDS plot in Fig. 3.8.16(d) is diffuse with little structure.

The INDSCAL method is now applied starting from random G matrices and the results are shown in Fig. 3.8.16(e) and (f) with the dendrogram cut level at its default value. The clustering is almost correct; all the samples are placed in the correct groups except that there are two outliers coloured in blue. Fig. 3.8.16(g) shows the Raman patterns for these samples: they are primarily background with very little usable signal.