1.       What is the number of possible clusterings of a data set of n points into k groups? What does this imply about the convergence behavior of algorithms whose objective function is guaranteed not to worsen from one iteration to the next?

2.       Implement the group-average linkage clustering algorithm.

3.       As discussed in the chapter, explicit feature engineering methods can be made faster and more accurate with Nystr¨om sampling. Spectral clustering has also been presented as a special case of kernel methods with explicit feature engineering in this chapter. Discuss the difficulties in using Nystr¨om sampling with spectral clustering. Can you think of any way of providing a reasonable approximation? [The second part of the question is open-ended without a crisp answer.