Suppose that the data mining task is to cluster points (with (x, y) representing location) into three clusters, where the points are A1(4, 8), A2(2, 4), A3(1, 7), B1(5, 4), B2(5, 7), B3(6, 6), C1(3, 7), C2(7, 8). The distance function is Euclidean distance. Suppose initially we assign A1, B1, and C1as the center of each cluster, respectively. Please use the k-means algorithmand show your R code.(a)the three cluster centers after the first round of execution. (b)the final points in the three clusters after the algorithm stops.

Explanation:

K- is the working procedure:

It takes n no. of predefined cluster as input and data points.

It also randomly initiate n centers of the clusters.

In this case the initial centers are given.

Steps you can follow

Step 1. Find distance of each data points from each centers.

Step 2. Assign each data point to the cluster with whose center is nearest to this data point.

Step 3. After assigning all data points calculate center of the cluster by taking mean of data points in cluster.

repeat above steps until the center in previous iteration and next iteration become same.

A1(4,8), A2(2, 4), A3(1, 7), B1(5, 4), B2(5,7), B3(6, 6), C1(3, 7), C2(7,8)

Centers are X1=A1, X2=B1, X3=C1

A1 will be assigned to cluster1, B1 will be assigned to cluster2 ,C1 will be assigned to cluster3.

Go through the attachment for the solution.

answerapplication;