A set of integers {11, 22, 3, 12, 1, 23, 21, 13, 2} is given.
a. Partition this given integer set into three clusters using K-means clustering, with
the following criteria:
i. The distance metric is Euclidean distance.
ii. The initial means for the three clusters are 1, 2 and 3 respectively (i.e. initial mean for cluster 1 is 1, initial mean for cluster 2 is 2 and that for cluster 3 is 3).
iii. The algorithm terminates when the means converge (i.e. the means are identical to those at the last iteration). Show clearly all the steps by giving the mean and its members for each cluster at every iteration. (3 marks)
b. If condition (ii) is changed in the sense that the initial means can be selected arbitrarily, then is it possible to yield clusters better than those obtained in (a)? If yes, suggest the best clusters (no need to show the steps). What can we say about the K-means algorithm from this?