Customer Spending $($in $$)$

C$1200$

C$2150$

C$3300$

C$4250$

C$5350$

C$6400$

C$7100$

C$880$

Suppose that the initial seeds $($centres of each cluster$)$ are C$1,$ C$4,$ and C$7.$ Run the k$-$means algorithm for $1$ epoch only.

In particular:

a$)$ Fill the distance matrix based on the Euclidean distance of the points given above:

C$1$ C$2$ C$3$ C$4$ C$5$ C$6$ C$7$ C$8$

C$10$

C$20$

C$30$

C$40$

C$50$

C$60$

C$70$

C$80$

b$)$ Calculate the cluster assignment at the end of the first epoch:

a$.$ The new cluster assignment $($i$.$e$.,$ contents of each cluster$)$

b$.$ The centroids of the new clusters

c$)$ How many more iterations are needed to converge? Show cluster assignments and

updated centroids for each of the remaining epochs.