▶Assignment step
Each point takes the label of its nearest current centroid.
K-Means: A Canonical Clustering Method
Alternate assignments and centroid updates
K-means partitions data into k groups by alternating between the nearest-center assignment and the centroid update.
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The essential idea: each iteration can only decrease the within-cluster squared-distance objective.
One Concept · One Example
What to notice
- Assignments are hard: every point gets one label.
- Centroids are means of assigned points.
- Initialization can change the final solution.
One objective, two alternating steps
Update step
Each centroid moves to the mean of the points carrying its label.
Watch k-means settle
Step through assignment and update phases, or restart from a new initialization.
K-means turns clustering into repeated nearest-center assignment and centroid recomputation.