Average-linkage cluster analysis

The problem lies in the model. The Euclidean distance calculation is inappropriate for use with correlated variables because it is based only on pairwise comparisons, without regard to the elongation of data point swarms along particular axes. In effect, Euclidean distance imposes a spherical constraint on the data set (18). When correlation has been removed from the data, (by derivation of standardized characteristic vectors) Euclidean distance and average-linkage cluster analysis return the three groups. 

Fig. 17.3. Tree displaying the relationships between the hexapeptide sequence patterns after cluster analysis of the pairwise distances between patterns using the method of average-linkage clustering...

Hierarchical cluster analysis (Section 6.4)—with the result represented by a dendrogram—is a complementary, nonlinear, and widely used method for cluster analysis. The distance measure used was dTANi (Equation 6.5), and the cluster mode was average linkage. The dendrogram in Figure 6.6 (without the chemical structures) was obtained from the descriptor matrix X by... 

FIGURE 6.6 Dendrogram from hierarchical cluster analysis (average linkage) of n = 20 standard amino acids. Distance measure used was dTANi (Equation 6.5) calculated from eight binary substructure descriptors. Four structure pairs with identical descriptors merge at a distance of zero. Clustering widely corresponds to the chemist s point of view. 

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. 

Fig. 2.15. The result of cluster analysis for IC influencing factors in Liaodong Bay sediments (Dendrogram nsing average linkage between groups, Pearson correlation)...

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