7. K-means. (15 points) You are given three data samples: (a) (5 points) Starting with K=2 cluster centers at 1=3 and 2=6, what are the cluster assignments and new cluster centers after K-means converges? What is the total cluster distance as defined by k=1KxiCkxik2 ? (b) (5 points) Find two initial cluster centers 1 and 2, that if you run K-means with K=2 using these initial cluster centers, it converges to two different cluster centers as compared to the previous question, and each cluster has at least one member. What is the total cluster distance? (c) (5 points) Suppose you want to use clustering for outlier detection. You find cluster means i,i=1,,K on the training data. Then, given a new data x and a threshold t, you declare x an outlier if xit for all i. Complete the following function to implement the outlier detection on a matrix of data x. The output is out [i]=1 if the sample x[i,:] is an outlier, and out [i]=0 otherwise. You must specify the other inputs of your function. Avoid for loops for full credit