2. (30 points) Given the following data points in 1D: x1 = 2, X2 = 4, 23 = 5, 24 = 8, 25 = 10, 26 = 12, perform k-means clustering algorithm for k = 2. (a) Start from initial cluster centers ci 0, C2 9. Show your steps for all iterations: (1) the cluster assignments Y1, ... , Y6; (2) the updated cluster centers at the end of that iteration. (b) How many iterations does it take for k-means algorithm to converge (i.e., number of iterations includes all iterations you perform to find convergence)? What is the reconstruction error (i.e., distortion measure J, equation 9.1 of the Bishop's textbook) at the end of that iteration? (c) Repeat the above steps with initial cluster centers C1 = 4, C2 = 10. (d) How many iterations does it take for k-means algorithm to converge in this case? What is the reconstruction error at the end of that iteration? (e) Comparing (a) with (c), which solution is better? Why? 2. (30 points) Given the following data points in 1D: x1 = 2, X2 = 4, 23 = 5, 24 = 8, 25 = 10, 26 = 12, perform k-means clustering algorithm for k = 2. (a) Start from initial cluster centers ci 0, C2 9. Show your steps for all iterations: (1) the cluster assignments Y1, ... , Y6; (2) the updated cluster centers at the end of that iteration. (b) How many iterations does it take for k-means algorithm to converge (i.e., number of iterations includes all iterations you perform to find convergence)? What is the reconstruction error (i.e., distortion measure J, equation 9.1 of the Bishop's textbook) at the end of that iteration? (c) Repeat the above steps with initial cluster centers C1 = 4, C2 = 10. (d) How many iterations does it take for k-means algorithm to converge in this case? What is the reconstruction error at the end of that iteration? (e) Comparing (a) with (c), which solution is better? Why