Consider the following $7$ two$-$dimensional observations:

Observation i

i $=1$ i$=2$ i$=3$ i$=4$ i$=5$ i$=6$ i$=7$

xi$1$

xi$2$

$1$

$4$

$1$

$3$

$1$

$2$

$5$

$1$

$2$

$3$

$6$

$2$

$4$

$1$

$1.$ Plot the observations in a two$-$dimensional graph.

$2.$ Perform K$-$means clustering with K $=2$ using the Euclidean norm. Toss a coin $7$

times to initialize the algorithm.

$3.$ Cluster the data using hierarchical clustering with complete linkage and the Euclidean

norm. Draw the resulting dendrogram