High-throughput powder diffraction. IV. Cluster validation using silhouettes and fuzzy clustering

In two previous papers [Gilmore, Barr & Paisley (2004). J. Appl. Cryst. 37, 231-242; Barr, Dong & Gilmore (2004). J. Appl. Cryst. 37, 243-252], it was demonstrated how to generate a correlation matrix by comparing full powder diffraction patterns, and then partition the diffractograms into groups using multivariate statistics and associated classification procedures. For clustering the patterns into related sets, dendrograms, metric multidimensional scaling and three-dimensional principal-components analysis score plots are employed. However, sometimes cluster membership for certain patterns is not always very clear or other ambiguities may arise; this paper describes cluster validation techniques using silhouettes and fuzzy clustering. The two methods operate in a complementary way: in some cases silhouettes are the most useful, and in others fuzzy clustering is more applicable. These procedures are available as options in the commercial computer program PolySNAP.