Problem $2.$ Given the following unlabelled dataset:

$x=\{x^{(i)}{\}}_i=1^9=\{23,52,29,37,46,47,32,25,49\}.$

$($a$)20\%$ Execute the K$-$centers algorithm with $K=3.$ The initial centroid is chosen as $x^{(7)}$;

show all your iterations. Then, compute the SSE and BSS of the resultant clustering.

$($b$)$

Execute the K$-$means algorithm with $K=3,$ where the initial centroid set is

$Z=\{x^{(7)},20,50\}$

Use no more than $8$ iterations; show all your steps. Then, compute the SSE and BSS of the

resultant clustering.

$($c

Calculate the dissimilarity matrix $D$ over $x.$ Thereby, execute the single linkage

algorithm. In each iteration, capture $($i$)$ the updated dissimilarity matrix and $($ii$)$

intermediate clustering results. Then, sketch its corresponding dendrogram.

THE END $-$