Exercise

1. Prove that the SSE converges with zero when we increase the number of desired clusters, K.
2. Using the example in this chapter, change the number of centroids and see how the final result varies.
3. What will happen if we move each cluster closer together?
4. There are multiple enhanced initialization methods of K-means. Let's try out the following initial centroids:
   • Forgy method: Choose K observations from the data points as centroids.
   • Random partition: Assign each data point to a cluster randomly.
5. Replace the naive K-means implementation that we used with the implementation in machinelearn.js.
6. It's not guaranteed that the K-means algorithm can be converged with the global optima. Illustrate where K-means only returns poor results.