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GATE DA 2026 Q36: First merge in agglomerative clustering with Manhattan distance

Question

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?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: D (official GATE 2026 final answer key)

Concept used: Agglomerative clustering first merges the closest pair; Manhattan distance is the sum of absolute coordinate differences.

First step: Distances: P1–P2 = 5, P2–P3 = 7, P3–P4 = 7, P2–P4 = 0 + 2 + 2 = 4, P1–P4 = 5, P1–P3 = 12.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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