Example$/$Exercise for k$-$means

$$ A firm has eight sales centers. The following pairs of points

show locations of centers on a two$-$dimensional grid.

$(8,9),(2,9),(8,6),(1,4),(4,2),(7,4),(4,9),(9,5)$

$$ The firm wants to use k$-$means clustering to find the

location of three supply depots and assign each sales

center to one supply depot, such that the distance from

depot to sales center is minimized.

$$ Starting with the following three randomly chosen initial

centroids as locations for the depots, apply the algorithm

until the location of depots and assignment of sales centers

is stable.

$(4\mathrm{.}52,4\mathrm{.}26),(7\mathrm{.}06,2\mathrm{.}13),(7\mathrm{.}99,6\mathrm{.}61)$