Limitations of the K$-$Means Algorithm I

$0/1$ point $($graded$)$

Remember that the K$-$Means Algorithm is given as below:

Randomly select

Iterate

Given $,$ assign each data point to the closest $,$ so that

Given find the best representatives $,$ i$.$e$.$ find such that

where is the number of points in $.$

Which of the following are false about K$-$Means Algorithm? Please choose all those apply.

found by the algorithm is always a partition of

It is always guaranteed that the representatives

The algorithm may output different and depending on the initialization of line $1$

Line $2\mathrm{.}2$ of the algorithm$($Given find the best representatives $...)$ finds the cost$-$minimizing representatives $.$