So let's make another data set.
In this case, you're going to pick three cluster centers and,
then, conveniently, we'll draw three clusters onto my diagram.
Obviously, for three cluster centers, you want a cluster to be here, right here,
and right over here.
So my question is, is it possible that all these data
points over here are represented by one cluster, and
these guys over here by two separate clusters.
Given what you know about k-means, do you think it can happen
that all these points here fall into one cluster and those two
fall into two clusters as one what's called a local minimum for clustering.