K- means clustering with scipy

K-means clustering is a method for finding clusters and cluster centers in a set of unlabeled data. Intuitively, we might think of a cluster as comprising a group of data points whose inter-point distances are small compared with the distances to points outside of the cluster. Given an initial set of K centers, the K-means algorithm alternates the two steps:

• for each center we identify the subset of training points (its cluster) that is closer to it than any other center;
• the means of each feature for the data points in each cluster are computed, and this mean vector becomes the new center for that cluster.

These two steps are iterated until the centers no longer move or the assignments no longer change. Then, a new point x can be assigned to the cluster of the closest prototype.
The Scipy library provides a good implementation of the K-Means algorithm. Let's see how to use it:

from pylab import plot,show
from numpy import vstack,array
from numpy.random import rand
from scipy.cluster.vq import kmeans,vq

# data generation
data = vstack((rand(150,2) + array([.5,.5]),rand(150,2)))

# computing K-Means with K = 2 (2 clusters)
centroids,_ = kmeans(data,2)
# assign each sample to a cluster
idx,_ = vq(data,centroids)

# some plotting using numpy's logical indexing
plot(data[idx==0,0],data[idx==0,1],'ob',
     data[idx==1,0],data[idx==1,1],'or')
plot(centroids[:,0],centroids[:,1],'sg',markersize=8)
show()

The result should be as follows:

In this case we splitted the data in 2 clusters, the blue points have been assigned to the first and the red ones to the second. The squares are the centers of the clusters.
Let's see try to split the data in 3 clusters:

# now with K = 3 (3 clusters)
centroids,_ = kmeans(data,3)
idx,_ = vq(data,centroids)

plot(data[idx==0,0],data[idx==0,1],'ob',
     data[idx==1,0],data[idx==1,1],'or',
     data[idx==2,0],data[idx==2,1],'og') # third cluster points
plot(centroids[:,0],centroids[:,1],'sm',markersize=8)
show()

This time the the result is as follows: