k-Means Clustering and Cluster Geometry Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

k-Means Clustering and Cluster Geometry short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Summary: Geometric Certainties

Voronoi Cells are intersections of half-spaces $\to$ Always Convex.
Convex Set Rule: If $a, b \in C_{k}$ , then $(1 - t) a + t b \in C_{k}$ for $t \in [0, 1]$ .
Midpoint Shortcut: $\frac{a + b}{2}$ is always in the same cluster as $a$ and $b$ .
Exam Tip: For "necessarily" questions, find the point on the segment connecting known cluster members.

Summary: Core Geometry Rules

$k$ -means partitions space into Voronoi cells.
Assignment step = constructing the Voronoi diagram.
Update step = moving centers to the centroid of their Voronoi cells.
Voronoi cells are always convex.
Boundaries are perpendicular bisectors between centers.
If points A and B are in the same cluster, the midpoint of A and B is also in that cluster.

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k-Means Clustering and Cluster Geometry Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

k-Means Clustering and Cluster Geometry short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice que

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