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Which of the following clustering representations and dendrogram depicts the use of MAX or complete link proximity function in hierarchical clustering?

A.   Q 20, Option A

B.  Q 20, Option B

C.  Q 20, Option C

D.  Q 20, Option D

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Answer: (B)

For the single link or MAX version of hierarchical clustering, the proximity of two clusters is defined as the maximum distance between any two points in the different clusters. Similarly, here points 3 and 6 are merged first. However, {3, 6} is merged with {4}, instead of {2, 5}. This is because the dist({3, 6}, {4}) = max(dist(3, 4), dist(6, 4)) = max(0.1513, 0.2216) = 0.2216, which is smaller than dist({3, 6}, {2, 5}) = max(dist(3, 2), dist(6, 2), dist(3, 5), dist(6, 5)) = max(0.1483, 0.2540, 0.2843, 0.3921) = 0.3921 and dist({3, 6}, {1}) = max(dist(3, 1), dist(6, 1)) = max(0.2218, 0.2347) = 0.2347.

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