Supervised Elements of Unsupervised Learning

$1$ point possible $($graded$)$

Remember that clustering is an example of unsupervised learning. However, unlike its name suggests, there

are some elements that we can "supervise" in clustering. In other words, there are some parts clustering that

needs to be determined or "tuned" by us$,$ depending on the application. Which of the following are elements of

clustering that we can and should tune, depending on the application?

Number of clusters $K$

$C_1,$dots,$C_K,$ the partition of $x_1,$dots,$x_n$

$z_1,$dots,$z_K,$ the representatives of each of the $K$ clusters

The cost measure for distance between $x^{(i)}in{C}_j$ and $)$