International Tables for Crystallography (2018). Vol. H, ch. 3.8, pp. 325-343
https://doi.org/10.1107/97809553602060000953

Chapter 3.8. Clustering and visualization of powder-diffraction data

Contents

  • 3.8. Clustering and visualization of powder-diffraction data  (pp. 325-343) | html | pdf | chapter contents |
    • 3.8.1. Introduction  (p. 325) | html | pdf |
    • 3.8.2. Comparing 1D diffraction patterns  (pp. 325-327) | html | pdf |
      • 3.8.2.1. Spearman's rank order coefficient  (p. 325) | html | pdf |
      • 3.8.2.2. Pearson's r coefficient  (p. 325) | html | pdf |
      • 3.8.2.3. Combining the correlation coefficients  (p. 325) | html | pdf |
      • 3.8.2.4. Full-profile qualitative pattern matching  (p. 326) | html | pdf |
      • 3.8.2.5. Generation of the correlation and distance matrices  (pp. 326-327) | html | pdf |
    • 3.8.3. Cluster analysis  (pp. 327-329) | html | pdf |
      • 3.8.3.1. Dendrograms  (p. 327) | html | pdf |
      • 3.8.3.2. Estimating the number of clusters  (pp. 327-328) | html | pdf |
      • 3.8.3.3. Metric multidimensional scaling  (pp. 328-329) | html | pdf |
      • 3.8.3.4. Principal-component analysis  (p. 329) | html | pdf |
      • 3.8.3.5. Choice of clustering method  (p. 329) | html | pdf |
      • 3.8.3.6. The most representative sample  (p. 329) | html | pdf |
      • 3.8.3.7. Amorphous samples  (p. 329) | html | pdf |
    • 3.8.4. Data visualization  (pp. 329-331) | html | pdf |
      • 3.8.4.1. Primary data visualization  (pp. 329-330) | html | pdf |
      • 3.8.4.2. Secondary visualization using parallel coordinates, the grand tour and minimum spanning trees  (pp. 330-331) | html | pdf |
        • 3.8.4.2.1. Parallel-coordinates plots  (pp. 330-331) | html | pdf |
        • 3.8.4.2.2. The grand tour  (p. 331) | html | pdf |
        • 3.8.4.2.3. Powder data as a tree: the minimum spanning trees  (p. 331) | html | pdf |
    • 3.8.5. Further validating and visualizing clusters: silhouettes and fuzzy clustering  (pp. 331-333) | html | pdf |
      • 3.8.5.1. Silhouettes  (pp. 331-333) | html | pdf |
      • 3.8.5.2. Fuzzy clustering  (p. 333) | html | pdf |
      • 3.8.5.3. The PolySNAP program and DIFFRAC.EVA  (p. 333) | html | pdf |
    • 3.8.6. Examples  (pp. 333-337) | html | pdf |
      • 3.8.6.1. Aspirin data  (pp. 333-335) | html | pdf |
        • 3.8.6.1.1. Aspirin data with amorphous samples included  (p. 335) | html | pdf |
      • 3.8.6.2. Phase transitions in ammonium nitrate  (pp. 335-337) | html | pdf |
    • 3.8.7. Quantitative analysis with high-throughput PXRD data without Rietveld refinement  (pp. 337-339) | html | pdf |
      • 3.8.7.1. Example: inorganic mixtures  (pp. 338-339) | html | pdf |
    • 3.8.8. Using spectroscopic data  (pp. 339-340) | html | pdf |
    • 3.8.9. Combining data types: the INDSCAL method  (pp. 340-342) | html | pdf |
      • 3.8.9.1. An example combining PXRD and Raman data  (p. 342) | html | pdf |
    • 3.8.10. Quality control  (p. 342) | html | pdf |
    • 3.8.11. Computer software  (p. 342) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 3.8.1. The use of the Pearson (r) and Spearman (R) correlation coefficients to quantitatively match powder patterns: (a) r = 0.93, R = 0.68; (b) r = 0.79, R = 0.90; (c) r = 0.66, R = 0.22  (p. 326) | html | pdf |
      • Fig. 3.8.2. Four different methods of estimating the number of clusters present in a set of 23 powder patterns for the drug doxazosin  (p. 327) | html | pdf |
      • Fig. 3.8.3. Example of a parallel-coordinates plot in six dimensions, with axes labeled X1, X2, …, X6, for a set of 80 organic PXRD samples partitioned into four clusters  (p. 330) | html | pdf |
      • Fig. 3.8.4. Flowchart for the cluster-analysis and data-visualization procedure described in this chapter  (p. 330) | html | pdf |
      • Fig. 3.8.5. Powder patterns for 13 commercial aspirin samples partitioned into five sets  (p. 331) | html | pdf |
      • Fig. 3.8.6. (a) The initial default dendrogram using the centroid clustering method on 13 PXRD patterns from 13 commercial aspirin samples  (p. 332) | html | pdf |
      • Fig. 3.8.7. The use of minimum spanning trees (MSTs)  (p. 333) | html | pdf |
      • Fig. 3.8.8. The use of silhouettes in defining the details of the clustering  (p. 334) | html | pdf |
      • Fig. 3.8.9. The complete cluster analysis for the aspirin samples  (pp. 335-336) | html | pdf |
      • Fig. 3.8.10. The aspirin data including data from five amorphous samples  (p. 337) | html | pdf |
      • Fig. 3.8.11. Ammonium nitrate phase transitions  (p. 338) | html | pdf |
      • Fig. 3.8.12. Identifying mixtures using lanthanum strontium copper oxide and caesium thiocyanate diffraction data taken from the ICDD Clay Minerals database  (p. 338) | html | pdf |
      • Fig. 3.8.13. (a) The dendrogram generated from 74 Raman spectra without background corrections applied  (p. 339) | html | pdf |
      • Fig. 3.8.14. Clustering the 74 Raman spectra without background corrections applied using first-derivative data  (p. 339) | html | pdf |
      • Fig. 3.8.15. A flowchart for the INDSCAL method using Raman and PXRD data  (p. 340) | html | pdf |
      • Fig. 3.8.16. Clustering 48 PXRD spectra with background corrections applied for three polymorphs of sulfathiazole  (p. 341) | html | pdf |
      • Fig. 3.8.17. Visualization tools for quality-control procedures using a modified MMDS plot  (p. 342) | html | pdf |
    • Tables
      • Table 3.8.1. Six commonly used clustering methods  (p. 327) | html | pdf |
      • Table 3.8.2. Estimate of the number of clusters for the 23 sample data set for doxazosin  (p. 328) | html | pdf |