Euclidean distance based π-means clustering algorithm was run on a dataset ofβ¦
2024
Euclidean distance based π-means clustering algorithm was run on a dataset of 100 points with π = 3. If the pointsΒ \(\begin{bmatrix} 1 \\ 1 \end{bmatrix} \) andΒ \(\begin{bmatrix} -1 \\ 1 \end{bmatrix} \) are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3?
- A.
\(\begin{bmatrix}0 \\0\end{bmatrix}\) - B.
\(\begin{bmatrix}0 \\2\end{bmatrix}\) - C.
\(\begin{bmatrix}2 \\0\end{bmatrix}\) - D.
\(\begin{bmatrix}0 \\1\end{bmatrix}\)
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Correct answer: D
The k-means algorithm assigns points to clusters based on Euclidean distance to cluster centroids. Given that [1, 1] and [-1, 1] are in cluster 3, their midpoint is [0, 1]. In k-means with Euclidean distance, points closer to the centroid are assigned to that cluster. The point [0, 1] lies exactly at the midpoint and is equidistant to both given points. Since it's on the line connecting them, it must be closer to their shared centroid than other options. Among all choices, [0, 1] is the only point that lies on this line and would be assigned to cluster 3 under standard k-means rules.