Assign to the Nearest Centroid - k-Means, One Honest Step

Assignment uses squared distance to each displayed centroid. The table keeps the starting centroid coordinates visible so every distance has a shown source.

highlighted = computed this step

Squared distance decides the assignment

For every point, the table recomputes d^2 to c1=(1, 1) and c2=(7, 7).

d^2=(x-c_x)^2+(y-c_y)^2

Nearest centroid

The first three points have distance 2 to c1. The last three have distance 2 to c2.

\text{assignments}=[c_1,c_1,c_1,c_2,c_2,c_2]

Summary

No square root is taken. Equal squared distances would use the lowest centroid index, so the assignment rule is deterministic.

\text{tie break}=\text{lowest centroid index}