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 average linkage distance between clusters A = {1,2} and B = {3,4}, we must average all pairwise distances between points in A and points in B.
List the cross-cluster distances: D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)=8. 
Add them up: 2 + 4 + 6 + 8 = 20. 
Now divide by the number of cross-pairs, which is 2 × 2 = 4: 20 / 4 = 5.0. 
Option a. 5.0 is therefore the correct average linkage distance.

Why the other choices are not correct:
- b. 4.0 would correspond to a different average or miscounted pairs; it does not match the actual sum 20 divided by 4.
- c. 3.5 would require a sum of 14 across 4 pairs, which is not the case with the given distances.
- d. 6.0 would imply a larger average than any single cross-pair distance or a miscalculation of the total pooled distance.

In summary, the average linkage distance is the mean of all cross-cluster distances, which here equals 5.0.

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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