Euclidean distance based k-means clustering algorithm was run on a dataset of 100 points with k = 3. If the points bmatrix 1 \\ 1 bmatrix and bmatrix -1 \\ 1 bmatrix are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3?

GATE DA 2024 Q19: Point necessarily in the same k-means cluster

Machine Learning
1 mark
MCQ
−1/3 if wrong

Euclidean distance based $k$ -means clustering algorithm was run on a dataset of 100 points with $k = 3$ . If the points $\begin{bmatrix} 1 \\ 1 \end{bmatrix}$ and $\begin{bmatrix} -1 \\ 1 \end{bmatrix}$ are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3?

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Answer: D (official GATE 2024 final answer key)

Concept used: Each $k$ -means cluster is the convex Voronoi cell of its centroid.

First step: A convex region containing $(1,1)$ and $(-1,1)$ contains the segment between them, which includes the midpoint $(0,1)$ .

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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 Q19: Point necessarily in the same k-means cluster

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