complete solution the pervious question $.$

$1.$ Suppose that the data mining task is to cluster points $($with $($x$,$ y$)$ representing location$)$ into three clusters, where the points are:

A$1(2,10),$A$2(2,5),$A$3(8,4),$ B$1(5,8),$B$2(7,5),$B$3(6,4),$ C$1(1,2),$C$2(4,9).$

The distance function is Euclidean distance. Suppose initially we assign A$1,$ B$1,$ and C$1$ as the center of each cluster, respectively. Use the k$-$means algorithm to show:

$($a$)$ The three cluster centers

$($b$)$ The final three clusters.

$2.$ Let's consider a dataset containing five data points represented by their coordinates:

Data Point X Y

Point $112$

Point $234$

Point $341$

Point $453$

Point $514($a$)$ Choose point $1$ and point $4$ as the initial medoids

$($b$)$ Calculate the dissimilarity between each data point and each medoid

$($c$)$ Assign points to nearest medoids