Cluster analysis complete linkage clustering

FIGURE 3.24 Dendrogram of fatty acid concentration data from mummies and reference samples. Hierarchical cluster analysis (complete linkage) with Euclidean distances has been applied. 

Twenty populations were sampled with plants from Hailuoto, at 65°00 N, representing the northernmost site and material from Hanko, at 59°49 N, representing the southernmost collection site (and, incidentally, the southernmost point of land in the country). Five samples represented central Finland with the remainder originating from the southern part. Fifty-five compounds were detected by GC-MS analysis, 53 of which were identified. The data obtained were subjected to complete linkage analysis, which differentiated several clusters that corresponded moderately well with geography. Genetic distance values derived from the RAPD data correlated well with chemical distance values determined from the terpene data (r=0.41, P<0.0001). 

Figure 2.13 Vhe use of cluster analysis to display the sisilarity of stationary phases with the complete linkage furthest neighbor dendrogras.

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).

In the first complete linkage analysis, the interaction term (layers, 1/1, float) was assigned the same weight as any of the other relevant attributes. The algorithm yielded three clusters (Figure 3) when there was only one match (or equivalently, when the maximum distance between clusters was 12 no matches ). Two of these clusters accounted for only 13 of the 101 location points. Interestingly, 11 of these 13 points were precisely those and only those points that revealed no pseudomorphs. The other two points were those for which pseudomorphic evidence could not be identified. As such, these two small clusters were taken together to form the cluster of inde-terminates . When matches were increased to three, the big cluster of 88 location points was subdivided into three smaller clusters. A cluster could represent either a fabric type or a fabric pattern. 

Figure 3. Complete linkage cluster analysis unweighted interaction.

Allen, F. H., Doyle, M. J., and Taylor, R. Automated conformational analysis from crystallographic data. 2. Symmetry-modified Jarvis-Patrick and complete-linkage clustering algorithms for three-dimensional pattern recognition. Acta Cryst. B47, 41-49 (1991). 

Allen, F.H. Doyle, M.J. Taylor, R. Automated Conformational Analysis from Crystallographic Data. 2 Symmefry-Modified Jarvis-Patrick and Complete-Linkage Clustering Algorithms for 3-D Pattern Recognition. Acta Crystallogr., 1991, B47, 41-49. 

Figure 3.3 Dendogram of clustering analysis for 131 tree species of the Mabira Forest Uganda (reference line at 30% similarity using complete linkage shovm) dataset.

Of the four different methods of cluster analysis applied, the method of Ward described in the Clustan User Manual (10), worked best when compared to the single-, complete-, or average-linkage methods. Using Ward s method, two clusters, Gn and Gm, are fused when by pooling the variance within two existing clusters the variance of the so formed clusters increases minimally. The variance or the sum of squares within the classes will be chosen as the index h of a partition. 

---