. (5 points) What's the main difference between supervised and unsupervised learning? Give one benet and drawback for supervised and unsupervised learning, respectly. . (5 points) Will different initializations for kmeans lead to different results? . (5 points) Give a short proof (can be in words but using correct logic) why kmeans algorithm will converge in nite number of iterations. . (5 points) What is the main dierence between kmeans and generalized kmeans algorithm? Explain how the choice of the similarity/ dissimilarity/ distance will impact the result. . (10 points) Consider the following simple graph 3%)! Write down the graph Laplacian matrix and nd the eigenvectors associated with the zero eigen- value. Explain how do you nd out the number of disconnected clusters in graph and identify these disconnected clusters using these eigenvectors