Watch K-means clustering step through centroid assignment and update. Adjust K, compare with random initialization, and visualize Voronoi cells.
Each step exposes the two operations that K-means normally hides: assigning points to their nearest centroid and moving each centroid to the mean of its assigned points. The canvas shows those changes together with the centroids' Voronoi cells, and random initialization makes it possible to compare different starting arrangements. The important surprise is that K-means does not discover the number of clusters. It produces exactly the selected K, and different initial centroids can produce different final partitions.
A concrete input and expected output from the current implementation.
Input
Set K to 1 and place points at (0, 0) and (2, 0).
Expected output
Both points belong to the single cluster, whose centroid is (1, 0). The visible plotting area is one Voronoi cell.
With K = 1, both points must share a cluster. Their coordinate mean is ((0 + 2) / 2, (0 + 0) / 2) = (1, 0), which confirms the displayed centroid.
At an assignment step, every plotted point joins the cluster whose current centroid is nearest in Euclidean distance. At an update step, each centroid moves to the arithmetic mean of the x- and y-coordinates assigned to it. Repeating these alternating steps reaches a stable assignment when another pass produces no change.
The Voronoi overlay partitions the visible plane by the current centroids. Every location inside one cell is closer to that cell's centroid than to the others, while a boundary marks equal distance between neighboring centroids. The cells move after centroid updates. Random initialization changes the starting centroids, so another run can settle on a different partition.
No. The alternating updates can stop at a result determined by the initial centroid positions, and another initialization may finish differently. Repeating the same point set with random initialization helps reveal that sensitivity. Even a compact-looking result is not proof that the selected K matches meaningful groups in the underlying subject.
A centroid is the coordinate-wise arithmetic mean of every point assigned to its cluster, not a selected representative point. That mean can fall between observations or even in an otherwise empty-looking area. Moving one distant observation may pull the centroid noticeably because every assigned point contributes to the mean.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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