Given the data set below, manually perform k-means clustering using Euclidean distance as the distance function. Here kis chosen as 3. The Euclidean distance in two dimensional space between two points (X, Y) and (x, Y) is calculated as: d=(x-x)+(-) The centers of the three clusters were initialized as = (6.2, 3.2) (red), (6.6, 3.7) (green) and 3 = (6.5, 3.0) (blue). Round all of your answers to this problem to three decimal places. X 5.9 4.6 6.2 4,7 5.5 5.0 4.9 6.7 5.1 6.0 y 3.2 2.9 28 3.2 4.2 3.0 3.1 3.1 3.8 H 3.0 a. What's the center of the red cluster after one iteration? b. What's the center of the green cluster after two iterations? c. What's the center of the blue cluster after three iterations? d. How many iterations are required for convergence to occur if the convergence criterion is no change to the centroids?