Tutorial Exercise $7$

Instructor: Namkiu Chan

For all the problems below, refer to the dataset shown as follows.

Problem $1.$ Using the $K-$centers algorithm discussed, cluster the dataset into $K=4$ groups. The

initiation of $z_1$ is set as $f.$ Write down the final clusters $C_1,$dots,$C_4$ and their representative vector

$Z=\{z_1,$dots,$z_4\}.$ Also, write down the radius $r(Z).$

Problem $2.$ Repeat Problem $1$ using the initiation of $z_1=d.$ Is there any difference?

Problem $3.$ Repeat Problem $1$ using $K=2,$ with an initiation of $z_1=d.$ What is $r(Z)?$

Problem $4.$ Let us now perform $K-$means clustering on the dataset. Suppose $K=3$ and the

initial centroids are $Z=\{a,e,h\}.$ Perform at most $5$ iterations. Compute the SSE and BSS

measurements.

Problem $5.$ Repeat Problem $4$ with initiation $Z=\{f,g,h\}.$ Perform at most $5$ iterations. Com$-$

pute the SSE and BSS measurements. What's the conclusion to be drawn here?