You have been provided with a dataset containing information about customer spending habits. Your task is to use the k$-$means algorithm with Euclidean distance to cluster the following $8$ examples into $3$ clusters:

$\backslash$table$[[$Customer$,$Spending $($in $$)],[$C$1,200],[$C$2,150],[$C$3,300]]$

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:

$\backslash$table$[[,$C$1,$C$2,$C$3,$C$4,$C$5,$C$6,$C$7,$C$8],[$C$1,0,,,,,,,],[$C$2,,0,,,,,,],[$C$3,,,0,,,,,],[$C$4,,,,0,,,,],[$C$5,,,,,0,,,],[$C$6,,,,,,0,,],[$C$7,,,,,,,0,],[$C$8,,,,,,,,0]]$

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.

In your report, you need to include the appropriate cluster assignment and centroids.