Impact of Initialization

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

Remember that the K$-$Means algorithm is given by

Randomly select

Iterate

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

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

Which of the following is true about the initialization and output of the K$-$Means algorithm? Select all those apply.

Step $2\mathrm{.}1$ decreases or does not change the cost of clustering output

Step $2\mathrm{.}2$ decreases or does not change the cost of clustering output

The clustering output that the K$-$Means algorithm converges to depends on the initialization