Problem $3K-$Means, $l_{}$ distance. $[10$pts$]$ Given the points over $3-$dimensional categorical data:

$(2,1,-1),(1,1,0),(3,-5,4)$

$(1,2,-1),(5,-1,2),(3,4,-5)$

$(6,5,-7),(1,2,5),(3,-2,3)$

$(1,1,2),(5,2,-4),(0,2,2)$

$(1,0,3),(4,3,-3),(2,-4,6)$

You need to use $l_{}$ norm as the distance measure. The $l_{}-$norm of a point $x=(x_1,x_2,$dots,$x_n)in{R}^n$ is defined to be

$||x|{|}_{}=ma{x}_i=1,2,$dots,$n|x_i|$

For example, the $l_{}-$norm of $(0,3,-4,1)$ is $4.$

Consider clustering them in $3$ clusters. The centroids are initialized at

$c_1=(1,0,4)$

$c_2=(-1,0,4)$

$c_2=(0,0,-3)$