Consider the following $10$ data points in a $2-$dimensional feature space:

$a(1,7)$;$b(2,7)$;$c(6,6)$;$d(3,5)$; $e(4,5)$; $f(3,4)$; $g(7,3)$; $h(1,2)$; $i(6,2)$; $j(3,1)$

This matrix represents the pairwise distances between each pair of points in the given set,

calculated using the Euclidean distance formula.

Suppose you are initializing $K-$means method, that is$,$ you initialize the cluster centers to $K$

randomly chosen data points. Let's assume that points $a(1,7),c(6,6)$ and $g(7,3)$ were

chosen. Perform one iteration of the K$-$means algorithm and report the coordinates of the

resulting centroids.

At the end of this epoch show:

a$)$ The new clusters $($i$.$e$.$ the examples belonging to each cluster$)$

b$)$ The centers of the new clusters

c$)$ How many more iterations are needed to converge?

Use single and complete link agglomerative clustering to group the data described by the

previous distance matrix. Show the dendrograms.