The GATE Grind

GATE 2025 DA – Question 30

Machine Learning · Unsupervised learning: clustering · 1 mark · Multiple select

Let $C_1$ and $C_2$ be two sets of objects. Let $D(x, y)$ be a measure of dissimilarity between two objects $x$ and $y$. Consider the following definitions of dissimilarity between $C_1$ and $C_2$.

$DIS\text{-}1(C_1, C_2) = \max_{x \in C_1, y \in C_2} D(x, y)$

$DIS\text{-}2(C_1, C_2) = \min_{x \in C_1, y \in C_2} D(x, y)$

Which of the following statements is/are correct?

  1. Single Linkage Clustering uses DIS-1
  2. Single Linkage Clustering uses DIS-2
  3. Complete Linkage Clustering uses DIS-2
  4. Complete Linkage Clustering uses DIS-1

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Show answer and explanation

Correct answer: (B) Single Linkage Clustering uses DIS-2; (D) Complete Linkage Clustering uses DIS-1

Explanation

Single linkage measures the distance between two clusters by their closest pair of points, which is the minimum (DIS-2). Complete linkage uses the farthest pair, which is the maximum (DIS-1). So B and D are correct.