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GATE 2026 DA Q.36: solution and answer

GATE 2026 · DAQ.36 · 2 marks · MCQ

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. (A)

    P1, P2

  2. (B)

    P2, P3

  3. (C)

    P3, P4

  4. (D)

    P2, P4

See the question in the paper
GATE 2026 DA question 36Tap to open full size

Answer and solution

ANSWER

The pair merged first is P2 and P4, at Manhattan distance 4, which is option (D).

Official answer: DSource: Official answer key, GATE 2026 DA (IIT Guwahati)

  1. Agglomerative clustering starts with every point as its own cluster, so the first merge joins the pair with the smallest pairwise distance. At this stage every cluster is a single point, so the linkage rule (single, complete or average) makes no difference.

  2. Manhattan distance is . There are pairs, so compute all six.

  3. .

  4. and .

  5. and .

  6. .

  7. The distances are . The smallest is , for and , so they merge first. This is option (D).

KEY IDEA

The first merge in agglomerative clustering takes the closest pair of individual points. The linkage rule only matters from the second merge onward, so just compute all pairwise distances in the stated metric and take the minimum.

WATCH OUT FOR

Using Euclidean distance instead of Manhattan, or dropping a minus sign when subtracting coordinates such as and . Another slip is to stop at the first small value, such as , without checking all six pairs. also has distance 5, and the true minimum is 4.

From the GATE 2026 DA paper. Every question of this paper · Download the full paper · All 4 Clustering questions, with notes

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