The two steps:
K-Means is a 2 step dance: Reassign data points & update centroid location.
Three things worth trying:
1. Packed circles, k = 4, and put all four centroids in one corner. About five times out of
six it gets stuck. That's why we chose starting algorithm such as: "Farthest Points."
2. Elongated data points, k = 2 — See how k-means is not appropriate for such datasets.
3. Try Smiley at k = 3. Same as above. K-means wasn't designed for such datasets.