- 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.

*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:

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