Procedure

randomly chose k centroids.

assign each observation to the nearest centroid (cluster).

calculate new means to be the centroids in the new clusters.

Initialization:

Assignment:

        Update:

Initialization

random.shuffle(observations)

centers = dict((c,[c]) for c in observations[:k])

centers[observations[k-1]] += observations[k:]

Assignment

for j in centers:
        for x in centers[j]:
            best = min(centers, key=lambda c: dist(x,c))
            new_centers[best] += [x]

Update

for j in centers:
        new_centers[mean(centers[j])] = centers[j]

Watch again!

Within-cluster Sum of Squares (WCSS)

Variance - Iteration chart