For the following $2-$D dataset, use Euclidean distance to answer the following questions

a$.$ Construct a complete$-$link hierarchical clustering for

the points in the dataset. Show your full dendrogram,

and illustrate how the points in the dataset will be

grouped into two clusters

$(5$ points$)$

b$.$ Assuming we start from cluster centroids p$1$ & p$2,$

trace $k-$means clustering with $k=2$ for $5$ iterations and

show how the points in the dataset are assigned to

the two clusters and how the centroids change

$(10$ points$)$

c$.$ Assuming that the results from hierarchical clustering

are the true assignments of the points $($their true

clusters$).$ Compute the precision and recall for the

k$-$means assignment with respect to the assumed true

classes of the points.

$(5$ points$)$

d$.$ Using expectation maximization, go through $2$

iterations of the algorithm by hand and compare your

output clustering with that of the hierarchical

clustering at different cut$-$offs for cluster assignment

$($you can go from $0$ to $1$ with $0\mathrm{.}1$ step$)$

$(10$ points$)$