Suppose s1 and s2 are randomly selected subsets from a

Question

Problem

1. Implement two versions of a simple k-means algorithm: one of which uses numerical centroids as centers, the other of which restricts centers to be input points from the data set. Then experiment. Which algorithm converges faster on average? Which algorithm produces clustrings with lower absolute and mean-squared error, and by how much?

2. Suppose s₁ and s₂ are randomly selected subsets from a universal set with n items. What is the expected value of the Jaccard similarity J(s₁, s₂)?