Implementation of K-Means Clustering on Randomly Generated Data with 5 Clusters

 

Experiment

Implementation of K-Means Clustering on Randomly Generated Data with 5 Clusters

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🎯 Objective

To generate sample data containing five clusters, apply the K-Means clustering algorithm, and visualize the clustering results.

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📘 Theory

🔹 K-Means Clustering

K-Means is an unsupervised learning algorithm that groups data points into K clusters based on similarity.

The algorithm attempts to minimize the distance between data points and their assigned cluster centroids.

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🔹 Working Steps of K-Means

1. Select the number of clusters (K)
2. Initialize K centroids
3. Compute distance of each point from all centroids
4. Assign points to nearest centroid
5. Compute new centroids
6. Repeat until convergence

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🔹 Objective Function

K-Means minimizes:

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

Where:

• $K$ = number of clusters
• $C_i$ = cluster $i$
  
• $\mu_i$= centroid of cluster $i$
  

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🧾 Dataset Description

Instead of using an external dataset, data points are generated randomly.

Characteristics:

• Total samples = 500
• Number of clusters = 5
• Features = 2
• Cluster centers generated automatically

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💻 Program

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score

# ------------------------------------
# Step 1: Generate random dataset
# ------------------------------------

X, y = make_blobs(
    n_samples=500,
    centers=5,
    n_features=2,
    random_state=42
)

# ------------------------------------
# Step 2: Visualize original data
# ------------------------------------

plt.figure()

plt.scatter(X[:,0], X[:,1])

plt.title("Randomly Generated Dataset")
plt.xlabel("Feature 1")
plt.ylabel("Feature 2")

plt.show()

# ------------------------------------
# Step 3: Apply K-Means
# ------------------------------------

k=5

kmeans = KMeans(
            n_clusters=k,
            init='k-means++',
            random_state=42
          )

labels = kmeans.fit_predict(X)

centroids = kmeans.cluster_centers_

# ------------------------------------
# Step 4: Compute metrics
# ------------------------------------

inertia = kmeans.inertia_

sil_score = silhouette_score(X,labels)

# ------------------------------------
# Step 5: Visualize clusters
# ------------------------------------

plt.figure()

plt.scatter(
            X[:,0],
            X[:,1],
            c=labels
           )

plt.scatter(
            centroids[:,0],
            centroids[:,1],
            marker='X',
            color='red'
            s=300
           )

plt.title("K-Means Clustering with K=5")
plt.xlabel("Feature 1")
plt.ylabel("Feature 2")

plt.show()

# ------------------------------------
# Step 6: Display output
# ------------------------------------

print("Centroids:\n")
print(centroids)

print("\nInertia:",inertia)

print("\nSilhouette Score:",sil_score)

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📊  Output

Centroids: [[-2.64387445 9.04103329] [-6.88093348 -6.9950069 ] [ 4.74346293 1.99434819] [-8.91925181 7.38961974] [ 2.13315564 4.35513167]] Inertia: 924.0989923406021 Silhouette Score: 0.678738720085253

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📈 Result Analysis

Inertia

• Measures compactness of clusters
• Lower value indicates tighter clusters

Silhouette Score

Interpretation:

Score	Meaning
Near +1	Well-separated clusters
Near 0	Overlapping clusters
Less than 0	Incorrect clustering

For this experiment:

Silhouette Score ≈ 0.7

This indicates good clustering quality.

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📌 Result

K-Means clustering was successfully applied on randomly generated data consisting of five clusters. The algorithm identified clusters and computed centroids successfully.