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 tackle the question, I’ll start by identifying all pairwise distances between elements of Cluster A = {1, 2} and Cluster B = {3, 4} under average linkage.
The relevant distances are:
- D(1,3) = 2
- D(1,4) = 4
- D(2,3) = 6
- D(2,4) = 8
Next, average linkage computes the mean of all these cross-cluster distances. Summing them gives 2 + 4 + 6 + 8 = 20. The number of cross-pairs between the two clusters is 4 (since 2 elements in A times 2 elements in B). Therefore, the average linkage distance is 20 / 4 = 5.0.
Now I compare this computed value to the provided options. Option a states 5.0, which matches the calculation exactly. Options b, c, and d correspond to 4.0, 3.5, and 6.0 respectively, which do not align with the computed average.
In short, the average of the four cross-cluster distances is 5.0, aligning with option a.

COMP9417-Machine Learning & Data Mining - T3 2025

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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