How to calculate k-means clustering with a numerical example?

Question

Use the k-means algorithm and Euclidean distance to cluster the following 8 examples into 3 clusters:

$A1=(2,10), A2=(2,5), A3=(8,4), A4=(5,8), A5=(7,5), A6=(6,4), A7=(1,2), A8=(4,9)$.

Suppose that the initial seeds (centers of each cluster) are $A1$, $A4$ and $A7$. Run the k-means algorithm for 1 epoch only. At the end of this epoch show:

a) The new clusters (i.e. the examples belonging to each cluster)

b) The centers of the new clusters

c) Draw a 10 by 10 space with all the 8 points and show the clusters after the first epoch and the new centroids.

d) How many more iterations are needed to converge? Draw the result for each epoch

Answer 1

The solution is also available here. I attached the solution for your information: