K-means clustering:-

Suppose that there are n records (or items) each with m attributes that can be expressed in numerical form, so that each item corresponds to a vector in m-dimensional space.

These can be grouped into k clusters with the k-means algorithm: First, k records are chosen as seeds.

Next, each other item is assigned to the seed closest to it in terms of Euclidean distance in the m-dimensional space. These assignments define k clusters.

Next, the centroid of each cluster is formed (being the point that minimizes the total squared distance to all points in the cluster), and these centroids replace the original seeds.

The algorithm then proceeds by reassigning each point to the centroid closest to it. This defines a revised clustering. The steps are repeated, calculating new centroids and obtaining new clusters, until the resulting change in clusters is small. Using this method, cluster the following items into two groups:

[2, 4, 10, 12, 3, 20, 30, 11, 25].

Begin by assigning the first two items as seeds, and arbitrarily assign 3 to the seed 2 (rather than to 4 since there is a tie).