Show that the clustering assignment problem

$($i$)=$ arg min

j$=1$;:::;k

kxi $$ cjk$2$

is equivalent to solving

$($i$)=$ arg min

j$=1$;:::;k

$($cj$)$T

$1$

$2$

cj $$ xi

:

Note that the second approach will facilitate $\backslash$vectorized$"$ operation and implemented in our demo

code.