How to do it...

Let's see how to perform a clustering data analysis using the k-means algorithm:

1. The full code for this recipe is given in the kmeans.py file that has already been provided to you. Now let's take a look at how it's built. Create a new Python file, and import the following packages:

import numpy as np 
import matplotlib.pyplot as plt 
from sklearn.cluster import KMeans 

1. Now let's load the input data and define the number of clusters. We will use the data_multivar.txt file that has already been provided to you:

input_file = ('data_multivar.txt')
# Load data
x = []
with open(input_file, 'r') as f:
    for line in f.readlines():
        data = [float(i) for i in line.split(',')]
        x.append(data)

data = np.array(x)
num_clusters = 4

1. We need to see what the input data looks like. Let's go ahead and add the following lines of code to the Python file:

plt.figure() 
plt.scatter(data[:,0], data[:,1], marker='o',  
        facecolors='none', edgecolors='k', s=30) 
x_min, x_max = min(data[:, 0]) - 1, max(data[:, 0]) + 1 
y_min, y_max = min(data[:, 1]) - 1, max(data[:, 1]) + 1 
plt.title('Input data') 
plt.xlim(x_min, x_max) 
plt.ylim(y_min, y_max) 
plt.xticks(()) 
plt.yticks(()) 

If you run this code, you will get the following output:

1. We are now ready to train the model. Let's initialize the kmeans object and train it:

kmeans = KMeans(init='k-means++', n_clusters=num_clusters, n_init=10) 
kmeans.fit(data)

1. Now that the data is trained, we need to visualize the boundaries. Let's go ahead and add the following lines of code to the Python file:

# Step size of the mesh 
step_size = 0.01 
 
# Plot the boundaries 
x_min, x_max = min(data[:, 0]) - 1, max(data[:, 0]) + 1 
y_min, y_max = min(data[:, 1]) - 1, max(data[:, 1]) + 1 
x_values, y_values = np.meshgrid(np.arange(x_min, x_max, step_size), np.arange(y_min, y_max, step_size)) 
 
# Predict labels for all points in the mesh 
predicted_labels = kmeans.predict(np.c_[x_values.ravel(), y_values.ravel()]) 

1. We just evaluated the model across a grid of points. Let's plot these results to view the boundaries:

# Plot the results 
predicted_labels = predicted_labels.reshape(x_values.shape) 
plt.figure() 
plt.clf() 
plt.imshow(predicted_labels, interpolation='nearest', 
           extent=(x_values.min(), x_values.max(), y_values.min(), y_values.max()), 
           cmap=plt.cm.Paired, 
           aspect='auto', origin='lower') 
 
plt.scatter(data[:,0], data[:,1], marker='o',  
        facecolors='none', edgecolors='k', s=30) 

1. Now let's overlay centroids on top of it:

centroids = kmeans.cluster_centers_ 
plt.scatter(centroids[:,0], centroids[:,1], marker='o', s=200, linewidths=3, 
        color='k', zorder=10, facecolors='black') 
x_min, x_max = min(data[:, 0]) - 1, max(data[:, 0]) + 1 
y_min, y_max = min(data[:, 1]) - 1, max(data[:, 1]) + 1 
plt.title('Centoids and boundaries obtained using KMeans') 
plt.xlim(x_min, x_max) 
plt.ylim(y_min, y_max) 
plt.xticks(()) 
plt.yticks(()) 
plt.show() 

If you run this code, you should see the following output:

The four centroids and their boundaries are sufficiently highlighted.