There is a set S consisting of six points in the plane shown as below, a = (0, 0), b = (8, 0), c = (16, 0), d = (0, 6), e = (8, 6), f = (16, 6). Now we run the k - means algorithm on those points with k = 3. The algorithm uses the Euclidean distance metric (i.e., the straight line distance between two points) to assign each point to its nearest centroid. Also we define the following:
• 3 - starting configuration is a subset of three starting points from S that form the initial centroids, for example, {a, b, c}.
• 3 - partition is a partition of S into k nonempty subsets, for example, {a, b, e}, {c, d}, {f} is a 3 - partition. (a) How many 3 - starting configurations are there? (b) Fill in the last two columns of the following table.