Three-distance clustering method

Fig. 30.11. The three-distance clustering method [23]. The new object A has to be classified. In node V a it must be decided whether it fits better in the group of nodes represented by Vi, the group of nodes represented by V2, or does not fit in any of the nodes already represented by V. ...

J. Zupan and D.L. Massart, Application of the three-distance clustering method in analytical chemistry. Anal. Chem., 61 (1989) 2098-2102. 

Unsupervised methods of pattern recognition have received less attention in spectrum interpretation. In one application to the interpretation of IR spectra, an ordered binary hierarchical tree was generated from a set of spectra of known compounds using the three-distance clustering method. There were no predefined substructures. 

Figure 6 A schematic representation of two clustering methods, m which each point represents a single molecular conformation and the circles are the similarity cutoff distances used to define the clusters, (a) Three clusters are defined when overlapping clusters are grouped together, (h) Five clusters are defined when the overlaps are removed from one of the overlapping clusters.

Compound selection is a core process of library design, and three main methods can be mentioned. Dissimilarity-based methods select compounds in terms of similar-ity/distance between individuals in chemical space. Clustering methods first group compounds into clusters based on similarity/distance and then choose representative compounds from different clusters. Partitioning methods first create a uniform cell space that subdivides the chemical space, then assign all virtual compounds to the relative cells according to their properties, and finally choose representative compounds from different cells. 

FIGURE 16.4 Results of a similarity-based compaiison producing a distance square matrix (lower window) on which two different clustering methods were applied. The top-left window represents a UPGMA tree where one additional criterion was printed (bands of one-dimensional electrophoresis profiles). The top-right window is a three-dimensional representation of the OTUs presented on the distance matrix below that have been reordered using the principal coordinate analysis ordination method. 

The biplot of Fig. 31.9 shows that both the centroids of the compounds and of the methods coincide with the origin (the small cross in the middle of the plot). The first two latent variables account for 83 and 14% of the inertia, respectively. Three percent of the inertia is carried by higher order latent variables. In this biplot we can only make interpretations of the bipolar axes directly in terms of the original data in X. Three prominent poles appear on this biplot DMSO, methylene-dichloride and ethylalcohol. They are called poles because they are at a large distance from the origin and from one another. They are also representative for the three clusters that have been identified already on the column-standardized biplot in Fig. 31.7. 

At present two three-dimensional structures are available, one determined by the 2D-NMR for solution protein (Cd,MT) and the other using the conventional crystallographic method . These are in conflict and major discrepancies exist between the two structures. In addition, in the recent crystallographic refinement where metal-sulphur clusters were also refined, metal-sulphur bond distances are obtained which are in serious error with respect to the EXAFS determined distances despite the claimed accuracy. For example, the Cd—S distances show considerable variation from 2.5 A the average terminal ligand distance is 3.2 A while the bridging... 

Figure 7.1 Authentication of monovarietal virgin olive oils results of applying clustering analysis to volatile compounds. The Mahattan (city block) distance metric and Ward s amalgamation methods were used in (a) the Squared Euclidean distance and (b) complete linkage amalgamation methods. Note A, cv. Arbequina (6) C, cv. Coratina (6) K, cv. Koroneiki (6) P, cv. Picual (6) 1, harvest 1991 2, harvest 1992. Olives were harvested at three levels of maturity (unripe, normal, overripe) (source SEXIA Group-Instituto de la Grasa, Seville, Spain).

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