GATE DA 2024 Set 1 — Question 19
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Machine Learning → Clustering → k-Means Clustering
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Question
Euclidean distance based -means clustering algorithm was run on a dataset of 100 points with . If the points and are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3?
Correct answer
(D) bmatrix 0 \ 1 bmatrix
Solution
In -means clustering using Euclidean distance, the clusters formed are Voronoi cells. A fundamental property of Voronoi cells is that they are convex sets. A set is convex if for any two points , the line segment connecting them is also entirely contained within . Given that and are in cluster 3, any point on the line segment between them must also be in cluster 3. The line segment is defined as .
For : Therefore, the point is necessarily part of cluster 3. Thus, option (D) is correct.
For : Therefore, the point is necessarily part of cluster 3. Thus, option (D) is correct.
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