Complete linkage method

There is a wide variety of hierarchical algorithms available and it is impossible to discuss all of them here. Therefore, we shall only explain the most typical ones, namely the single linkage, the complete linkage and the average linkage methods. 

There exist several methods of hierarchical clustering which use diverse measures of distance or similarity, respectively, e.g., single linkage, complete linkage, average linkage, centroid linkage, and Ward s method (Sharaf et al. [1986], Massart et al. [1988], Otto [1998] Danzer et al. [2001]). 

Compute the distances between all clusters using complete linkage, single linkage, average linkage, or other methods. 

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. 

Figure 6. Heat map of a small cluster of related antihistaminic drugs. 149 pharmacological assays are clustered on the X-axis and 10 compounds are clustered on the Y-axis. Clustering is performed using Pearson correlation and complete linkage using a pICso data set. For nonhits with primary screening % inhibition values of less than 20%, a default pICso value of 3.5 was used. Non-hits and above 20% inhibition received a default pICso value of 4.0. The pICso values range from the default value of 3.5 (blue-green) to 9 (red). Black spaces indicate data that is missing due to compound interference with the detection method.

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).

---