mplement K$-$means manually.

Figure $1$: Scatter plot of datasets and the initialized centers of $3$ clusters

Given the input matrix $$ whose rows represent different data points, please perform a k$-$means

clustering on this dataset using the Euclidean distance as the distance function. Here $$ is chosen

as $3.$ The Euclidean distance d between input vector $$ in $$ and $$ in $$ is defined as

$=()$

$$

$$

All data in X were plotted in Figure $1.$ The center of $3$ clusters were initialized as $=(6\mathrm{.}2,3\mathrm{.}2)$

$($red$),=(6\mathrm{.}6,3\mathrm{.}7)($green$),=(6\mathrm{.}5,3\mathrm{.}0)($blue$).$

a$.$ What are $3$ clusters and their centers after one iteration? Show the detailed steps, same as

questions b$.[15$ pts$]$

b$.$ What are $3$ clusters and their centers after two iterations?