In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

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BlackTom AI · Accepted Answer

To determine the average linkage distance between clusters A = {1, 2} and B = {3, 4}, we take all pairwise distances between points in A and points in B and compute their average.
First, list the cross-cluster distances: D(1,3) = 2, D(1,4) = 4, D(2,3) = 6, D(2,4) = 8. Then sum these values: 2 + 4 + 6 + 8 = 20.
Next, count how many cross-cluster pairs there are: since A has 2 elements and B has 2 elements, there are 2 × 2 = 4 pairs.
Now compute the average: 20 / 4 = 5.0. This is the distance used in average linkage when merging these two clusters.
Option a. 5.0: This matches the computed average correctly.
Option b. 4.0: This would imply a smaller mean, perhaps if one of the distances were different or if only a subset of pairs were used.
Option c. 3.5: This would require a sum of 14 over 4 pairs, which is not the actual total of the given distances.
Option d. 6.0: This would occur if the average were computed over a different count or if higher values dominated the mean; with the four cross-cluster distances provided, 6.0 would be inconsistent with the data.

In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

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