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Chapter 12. Reports WPGAMA Weighted pair group method using arithmetic averages. This is also called Average Linkage. d ki = 0.5 ⋅ d pi + 0.5 ⋅ d qi WPGAMA is a special case of UPGAMA that favors the most recent member clusters in forming new clusters. Centroid nq np ( n p ⋅ nq ) d ki = ⎛ -----⎞ ⋅ d pi + ⎛ -----⎞ ⋅ d qi – ------------------⎝ n⎠ ⎝ n⎠ n 2 d pq Median d ki = 0.5 ⋅ d pi + 0.5 ⋅ d qi – 0.25 ⋅ d pq Centroid and Median are similar to UPGAMA and WPGAMA, respectively, but the distance formula contains an additional third term. Centroid and Median methods are not monatomic hierarchical clustering algorithms. In other words, the similarity value between cluster k and any other cluster may be greater than the similarity between cluster p and cluster q. This condition occurs if the centroids (or medians) of the different clusters have approximately the same distance as the distances between the samples that make up the cluster. Ward's This method attempts to minimize the information by describing a set of N samples using a fewer number of clusters. np + ni nq + ni ni d ki = ---------------- d pi + ---------------- d qi – ------------- d pq n + ni n + ni n + ni 12-17
