Impact of Initialization

$\frac{0}{1}$ point $($graded$)$

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

Randomly select $z_1,$dots,$z_K$

Iterate

Given $z_1,$dots,$z_K,$ assign each data point $x^{(i)}$ to the closest $z_j,$ so that

Cost$(z_1,dots{z}_K)={\displaystyle \underset{i=1}{\overset{n}{}}}mi{n}_j=1,$dots,$k||x^{(i)}-z_j|{|}^2$

Given $C_1,$dots,$C_K$ find the best representatives $z_1,$dots,$z_K,$ i$.$e$.$ find $z_1,$dots,$z_K$ such that

$z_j=argmi{n}_z{\displaystyle \underset{iin{C}_j}{\overset{?}{}}}||x^{(i)}-z|{|}^2$

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

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Incorrect $(0/1$ point$)$