Given the samples X1 = {1, 0}, X2 = {0, 1}, X3 = {2, 1}, and X4 = {3, 3}, suppose that the samples are randomly clustered into two clusters C1 = {X1, X3} and C2 = {X2, X4}. (a) Apply one iteration of...

Given the samples X1 = {1, 0}, X2 = {0, 1}, X3 = {2, 1}, and X4 = {3, 3}, suppose that the samples are randomly clustered into two clusters C1 = {X1, X3} and C2 = {X2, X4}.

(a) Apply one iteration of the K - means partitional - clustering algorithm, and fi nd a new distribution of samples in clusters. What are the new centroids? How can you prove that the new distribution of samples is better than the initial one?

(b) What is the change in the total square - error?

(c) Apply the second iteration of the K - means algorithm and discuss the changes in clusters.