Mastering K-means Clustering and the Rand Index with Python

Introduction and Overview

Welcome back! In this lesson, we're seeking a more in-depth understanding of the K-means clustering algorithm by using a straightforward 2D dataset. We'll explore its implementation and evaluate its performance using a well-known measure of clustering accuracy: the Rand Index .

Understanding the Rand Index

RI = \frac{TP + TN} {TP+FP+FN + TN}

Rand Index vs Adjusted Rand Score

ARI = \frac {RI - Expected\_RI} {Max\_RI - Expected\_RI}

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Full Implementation: K-means and Evaluating with the Adjusted Rand Score using sklearn

With all the pieces at hand, let's put everything together. We'll perform K-means clustering on our toy dataset using sklearn's KMeans function, then evaluate the results using the adjusted Adjusted Rand Score from sklearn. Here's how to do that:

First we initialize the data and perform clustering:

Python

import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.metrics import adjusted_rand_score
np.random.seed(42)

# Define a 2D dataset and true labels for assessment
features = np.array([[1, 1], [1, 2], [2, 1], [2, 2], 
                     [5, 5], [5, 6], [6, 5], [6, 6], 
                     [9, 9], [9, 10], [10, 9], [10, 10],
                     [10, 2], [10, 3], [11, 2], [11, 3], 
                     [4, 8], [4, 9], [5, 8], [5, 9], 
                     [3, 5], [3, 6], [3, 5], [3, 6]])
true_labels = np.array([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2])

# Define the K-means algorithm and fit the model to the data
kmeans = KMeans(n_clusters=3, n_init=10, random_state=42)
kmeans.fit(features)

import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.metrics import adjusted_rand_score
np.random.seed(42)

# Define a 2D dataset and true labels for assessment
features = np.array([[1, 1], [1, 2], [2, 1], [2, 2], 
                     [5, 5], [5, 6], [6, 5], [6, 6], 
                     [9, 9], [9, 10], [10, 9], [10, 10],
                     [10, 2], [10, 3], [11, 2], [11, 3], 
                     [4, 8], [4, 9], [5, 8], [5, 9], 
                     [3, 5], [3, 6], [3, 5], [3, 6]])
true_labels = np.array([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2])

# Define the K-means algorithm and fit the model to the data
kmeans = KMeans(n_clusters=3, n_init=10, random_state=42)
kmeans.fit(features)

Now lets calculate the Adjusted Rand Score using sklearn:

Python

# Obtain the labels
labels = kmeans.labels_

# Calculate the Adjusted Rand Score using sklearn
ri = adjusted_rand_score(true_labels, labels)

# Output the resulting cluster labels, centroids and Adjusted Rand Score
print("Cluster labels: ", labels)
print("Centroids: ", kmeans.cluster_centers_) # Prints [[3.0 4.0] [10.5 2.5] [6.8 8.6]]. Might be different depending on the lib versions.
print("Adjusted Rand Score: ", ri) # Prints ~ 0.12 Might be different depending on the lib versions.

# Visualizing the clusters
plt.scatter(features[:, 0], features[:, 1], c=labels)
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], c='red')
plt.title("Clusters with Centroids (Red)")
plt.show()

# Obtain the labels
labels = kmeans.labels_

# Calculate the Adjusted Rand Score using sklearn
ri = adjusted_rand_score(true_labels, labels)

# Output the resulting cluster labels, centroids and Adjusted Rand Score
print("Cluster labels: ", labels)
print("Centroids: ", kmeans.cluster_centers_) # Prints [[3.0 4.0] [10.5 2.5] [6.8 8.6]]. Might be different depending on the lib versions.
print("Adjusted Rand Score: ", ri) # Prints ~ 0.12 Might be different depending on the lib versions.

# Visualizing the clusters
plt.scatter(features[:, 0], features[:, 1], c=labels)
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], c='red')
plt.title("Clusters with Centroids (Red)")
plt.show()

Here, we have effectively encapsulated our prior discussions on implementing K-means clustering, applying the Adjusted Rand Score, and bringing the insights to life through visual representations. Sklearn's KMeans function simplifies the K-means process into merely defining the model, fitting it to the data, and performing evaluations. By reflecting this streamlined process, the code highlights the importance of understanding essential concepts, navigating libraries, and connecting functions to their origins.

Introduction and Overview

Understanding the Rand Index

Rand Index vs Adjusted Rand Score

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Evaluating K-means with the Adjusted Rand Score using sklearn

Full Implementation: K-means and Evaluating with the Adjusted Rand Score using sklearn

Lesson Summary and Practice