A quick but detailed soultion please, the last answer to this question did not have enough detail, i have done part a just need part b and c in detail. I.E the exact working out for each step, when calcuating the clutser, i have got this answer which seems incorrect can you point my mistake out, so c$2$ is $150$ and you subtract it from c$1,$ c$4$ and c$7$ respectively which are $200,250,100$ and you get the answer $50,100,50$ you then choose the lowest one at random and i chose for c$2$ to be assigned with c$1$ so the k$1$ cluster you then calculate the new mean which is $200+150$ divide by $2$ then you assign c$3$ to a cluster which is $300$ so you subtract $300-175$ which is c$1$ and c$2$ mean then $300-$the mean of k$2$ which is c$4250$ and k$3$ which is c$7$ and $100$ the answers you get is $125,50,200$ you assign c$3$ to c$4$ and calculate the mean which is $250+300$ divide by $2$ equals $275$ now for c$5$ which is $350,$ k$1$ which is $175$ which is subtracted from $350$ then k$2$ which is $275$ subtracted from $350$ then k$3$ which is $100$ subtracted from $350$ equals $50$ assign to k$2$ and calculate new mean which is $250+300+275$ divide by $3$ giving $275$ now for c$6$ which is $400$ try with k$1400-175$ equals $225$ then for k$2400-275$ equals $125$ and similarly for k$3400-100=300$ assign to k$2$ new mean for k$2$ is now $275+400+300+250$ divide by $4$ equals $306\mathrm{.}25,$ now for c$8$ which is $80$ k$1$ which is $175$ subtract $80$ equals $95$ k$2$: $306\mathrm{.}25-80=226\mathrm{.}25,$ k$3$ which is $100-80$ equals $20$ answer is $20$ assign to c$7,$ why has the algorithm converged show reasons why, why can a second epoch not occur?

Question $4$B $-$ Clustering $[25\%]$

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$3,300]]$

$\backslash$table$[[C4,250],[C5,350],[C6,400],[C7,100],[C8,80]]$

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.