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GATE 2026 DA – Question 36

Machine Learning · Unsupervised learning: clustering · 2 marks · Multiple choice

Let four points in three-dimensional space be:

P1: [2, 3, -1], P2: [3, 1, 1], P3: [5, -2, 3] and P4: [3, 3, 3].

Hierarchical Agglomerative Clustering is used to cluster the above points. If Manhattan Distance is used as the distance metric during clustering, which of the following options indicates the two points that will be merged first?

  1. $P_1, P_2$
  2. $P_2, P_3$
  3. $P_3, P_4$
  4. $P_2, P_4$

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Correct answer: (D) $P_2, P_4$

Explanation

Agglomerative clustering first merges the two closest points. The Manhattan distances (sum of absolute differences of the coordinates) are: P1-P2 $= 1 + 2 + 2 = 5$, P1-P3 $= 3 + 5 + 4 = 12$, P1-P4 $= 1 + 0 + 4 = 5$, P2-P3 $= 2 + 3 + 2 = 7$, P2-P4 $= 0 + 2 + 2 = 4$ and P3-P4 $= 2 + 5 + 0 = 7$. The smallest is 4, for P2 and P4.