Please organise well the answer with intermediate steps well and formula's in the answer. Thank you

Problem $4.$

$[$A$]$ Clustering $K-$aleans $.$

$[27]$ 'Run' $5-$means manually for the dataset on

Figure $1.$ Dots are data points and darkened circles $C{l}_1,C{2}_2,C_3{C}_4,$ and $C_5$ are the initial cluster

centers. Depict the result of successive iterations of $5-$means on a successive pictures below, L$.$e$.$

each of nine repeated pictures below may correspond to an iteration of $5-$means. At each iteration

draw the position of cluster centers and the decision boundaries that define each cluster at this

iteration.

Note: Please remember, that in classic $k-$means algorithm if a cluster center has no points assigned

to it$,$ it stays where it is for that iteration.

FISH BELOW CORRESPOND TO ONE ITERATION. USE PICTURES TO SHOW

ITERATION RESULTS

Caution: The fact that there are $9$ pictures does not mean that there are $9$ iterations before

convergence. It only means that on this data set the algorithm converges in at most $9$ steps.

Figure $1$: Dataset for problem $4-K-$means.