The plotted view shows the same computed step geometrically. Points are colored by assignment, old centroids are squares, and updated centroids are diamonds.
highlighted = computed this step
The same step on the plot
The plot colors points by their recomputed assignment. Squares mark the old centroids and diamonds mark the exact updated means.
old squares → new diamonds \text{old squares}\rightarrow\text{new diamonds} old squares → new diamonds One plotted step Old centroids and updated exact means are shown together. one exact centroid update old c1=(1,1) old c2=(7,7) new c1=(2/3,2/3) new c2=(20/3,20/3) squares are old centroids; diamonds are exact means after one update one exact assignment-update timeline one static sequence: start centroids -> assign by d^2 -> recompute exact means 1. start c1=(1,1) c2=(7,7) k=2; starting centroids only 2. assign nearest smaller d^2 point d^2 pair to (0,0) (2,98) c1 (2,0) (2,74) c1 (0,2) (2,74) c1 (6,6) (50,2) c2 (6,8) (74,2) c2 (8,6) (74,2) c2 3. recompute c1 count=3 sum=(2,2) c1'=(2/3,2/3) c2 count=3 sum=(20,20) c2'=(20/3,20/3) one update only; no convergence claim
What moves
The left centroid moves from (1, 1) to (2/3, 2/3). The right centroid moves from (7, 7) to (20/3, 20/3).
c 1 ′ , c 2 ′ are exact means c_1',c_2'\text{ are exact means} c 1 ′ , c 2 ′ are exact means One plotted step Old centroids and updated exact means are shown together. one exact centroid update old c1=(1,1) old c2=(7,7) new c1=(2/3,2/3) new c2=(20/3,20/3) squares are old centroids; diamonds are exact means after one update one exact assignment-update timeline one static sequence: start centroids -> assign by d^2 -> recompute exact means 1. start c1=(1,1) c2=(7,7) k=2; starting centroids only 2. assign nearest smaller d^2 point d^2 pair to (0,0) (2,98) c1 (2,0) (2,74) c1 (0,2) (2,74) c1 (6,6) (50,2) c2 (6,8) (74,2) c2 (8,6) (74,2) c2 3. recompute c1 count=3 sum=(2,2) c1'=(2/3,2/3) c2 count=3 sum=(20,20) c2'=(20/3,20/3) one update only; no convergence claim
Summary
This is one plotted assignment-and-update step. The plot is not an iteration history.
one step only \text{one step only} one step only One plotted step Old centroids and updated exact means are shown together. one exact centroid update old c1=(1,1) old c2=(7,7) new c1=(2/3,2/3) new c2=(20/3,20/3) squares are old centroids; diamonds are exact means after one update one exact assignment-update timeline one static sequence: start centroids -> assign by d^2 -> recompute exact means 1. start c1=(1,1) c2=(7,7) k=2; starting centroids only 2. assign nearest smaller d^2 point d^2 pair to (0,0) (2,98) c1 (2,0) (2,74) c1 (0,2) (2,74) c1 (6,6) (50,2) c2 (6,8) (74,2) c2 (8,6) (74,2) c2 3. recompute c1 count=3 sum=(2,2) c1'=(2/3,2/3) c2 count=3 sum=(20,20) c2'=(20/3,20/3) one update only; no convergence claim