You are given two sets of 100 points that fall within the unit square. One set of points is arranged so that the points are uniformly spaced. The other set of points is generated from a uniform distribution over the unit square.
(a) Is there a difference between the two sets of points?
Yes. The random points will have regions of lesser or greater density, while the uniformly distributed points will, of course, have uniform density throughout the unit square.
(b) If so, which set of points will typically have a smaller SSE for K=10 clusters?
The random set of points will have a lower SSE.
(c) What will be the behavior of DBSCAN on the uniform data set? The random data set?
DBSCAN will merge all points in the uniform data set into one cluster or classify them all as noise, depending on the threshold. There might be some boundary issues for points at the edge of the region. However, DBSCAN can often find clusters in the random data, since it does have some variation in density.