• 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.

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.
(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.
Note: Do not get distracted by special cases or bring in factors other than
density. However, if you feel the true answer is different from any given
above, justify your response.

The correct answer is (c). Less dense regions require more centroids if the
squared error is to be minimized.