Suppose that for a data set

• There are m points and K clusters,

• Half the points and clusters are in “more dense” regions,

• Half the points and clusters are in “less dense” regions, and

• The two regions are well-separated from each other. Which of the following should occur to minimize the squared error when finding K clusters:

(a) Centroids should be equally distributed between more dense and less dense regions.

(b) More centroids should be allocated to the less dense region.

(c) More centroids should be allocated to the denser region. Explain: