Implement K-Means Clustering with Scipy on Random Data

K-means clustering algorithm, also called flat clustering, is a method of computing the clusters and cluster centers (centroids) in a set of unlabeled data. It iterates until we find the optimal centroid. The clusters, we might think of a group of data points whose inter-point distances are small as compared to the distances to the point outside of that cluster. The number of clusters identified from unlabeled data is represented by ‘K’ in K-means algorithm.

Given an initial set of K centers, the K-means clustering algorithm can be done using SciPy library by executing by the following steps −

Step1− Data point normalization

Step2− Computing the Centroids which is referred to as code. Here, the 2-dimensional array of centroids is referred to as a code book.

Step3− Cluster formation and assigning the data points. It is referred to as mapping from the code book.

Example

#importing the required Python libraries :
import numpy as np
from numpy import vstack,array
from numpy.random import rand
from scipy.cluster.vq import whiten, kmeans, vq
from pylab import plot,show

#Random data generation :
data = vstack((rand(200,2) + array([.5,.5]),rand(150,2)))

#Normalizing the data :
data = whiten(data)

# computing K-Means with K = 2 (2 clusters)
centroids, mean_value = kmeans(data, 2)
print("Code book :
", centroids, "
")
print("Mean of Euclidean distances :", mean_value.round(4))

# mapping the centroids
clusters, _ = vq(data, centroids)
print("Cluster index :", clusters, "
")
#Plotting using numpy's logical indexing
plot(data[clusters==0,0],data[clusters==0,1],'ob',data[clusters==1,0],data[clusters==1,1],'or')
plot(centroids[:,0],centroids[:,1],'sg',markersize=8)
show()

Output

Code book :
[[2.68379425 2.77892846]
[1.34079677 1.27029728]]


Mean of Euclidean distances : 0.9384

Cluster index : [0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 1 1 0
0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1
1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1
1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0
1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1
1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0]