Implementation of K-Means Clustering Using Scikit-Learn

 

Experiment

Implementation of K-Means Clustering Using Scikit-Learn

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🎯 Objective

To implement the K-Means clustering algorithm using scikit-learn and visualize how data points are grouped into clusters.

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📘 Theory

🔹 Clustering

Clustering is an unsupervised learning technique used to group similar data points based on their features.

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🔹 K-Means in Scikit-Learn

The KMeans class from sklearn.cluster provides an efficient implementation of the K-Means algorithm.

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🔹 Working Principle

1. Specify number of clusters K
2. Algorithm initializes centroids (random or k-means++)
3. Assigns points to nearest centroid
4. Updates centroids iteratively
5. Stops when centroids stabilize

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🔹 Objective Function

K-Means minimizes:

$$J = \sum_{i=1}^{K} \sum_{x \in C_i} ||x - \mu_i||^2$$

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🧾 Sample Dataset

Point	X	Y
P1	2	3
P2	3	4
P3	3	3
P4	8	7
P5	7	8
P6	8	8
P7               22		30

P8               25     30

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💻 Program (Python Code Using Scikit-Learn)

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

# Step 1: Dataset
X = np.array([
    [2, 3],
    [3, 4],
    [3, 3],
    [8, 7],
    [7, 8],
    [8, 8],
    [22,28],
    [25, 30]
])

# Step 2: Define number of clusters
k = 3

# Step 3: Apply K-Means
kmeans = KMeans(n_clusters=k, init='k-means++', random_state=0)
kmeans.fit(X)

# Step 4: Get labels and centroids
labels = kmeans.labels_
centroids = kmeans.cluster_centers_

# Step 5: Visualization
plt.scatter(X[:, 0], X[:, 1], c=labels)

# Plot centroids
plt.scatter(centroids[:, 0], centroids[:, 1], 
            marker='X', s=200, c='red')

plt.title("K-Means Clustering (Scikit-Learn)")
plt.xlabel("X")
plt.ylabel("Y")
plt.show()

# Step 6: Output
print("Cluster Labels:", labels)
print("Centroids:\n", centroids)

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📊 Output

🔹 Cluster Labels 

Cluster Labels: [2 2 2 0 0 0 1 1]

🔹 Centroids 

Centroids:
 [[ 7.66666667  7.66666667]
 [23.5        29.        ]
 [ 2.66666667  3.33333333]]

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📌 Result

The K-Means algorithm using scikit-learn successfully grouped the dataset into 3 clusters, and the centroids were computed automatically.

• scikit-learn simplifies implementation of K-Means
• Efficient for large datasets
• Automatically handles centroid initialization (k-means++)