GATE DA 2024 Q42: Dendrogram from single-linkage clustering

Machine Learning
2 marks
MCQ
−2/3 if wrong

Consider the table below, where the $(i, j)^{th}$ element of the table is the distance between points $x_i$ and $x_j$ . Single linkage clustering is performed on data points $x_1, x_2, x_3, x_4, x_5$ .

	$x_1$	$x_2$	$x_3$	$x_4$	$x_5$
$x_1$	0	1	4	3	6
$x_2$	1	0	3	5	3
$x_3$	4	3	0	2	5
$x_4$	3	5	2	0	1
$x_5$	6	3	5	1	0

Four dendrograms labelled A to D over points x1 to x5 — Tap the figure to enlarge

Which ONE of the dendrograms (A) to (D) in the figure above is the correct representation of the clusters produced?

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: A (official GATE 2024 final answer key)

Concept used: Single linkage: merge the two clusters whose closest members are nearest, repeatedly.

First step: Merge $\{x_1,x_2\}$ and $\{x_4,x_5\}$ at distance 1, then $x_3$ joins $\{x_4,x_5\}$ at 2, then the two groups join at 3.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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GATE DA 2024 Q42: Dendrogram from single-linkage clustering

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