The clusters that K-means clustering generates depend on the randomly chosen initial values. Repeat ten times to find the sequence of values immediately after the 2-step update. Display each transition as a line graph on the same graph.
K-means clustering minimizes 
w.r.t. C1,…,CK from data
X = (xi,j)
(a) Show the following equation:
(b) Show that the score S is monotonously decreasing each time the two steps are executed in Problem
(c) Let N = 3, p = 1, and K = 2, and assume that the samples are in 0, 6, 10. We consider two cases: one and two are assigned to 0, 6 and 10, respectively; and one and two are assigned to 0 and 6, 10, respectively. What values do they converge to if the initial state is each of the two cases? What score do they finally obtain?
