Unsupervised Learning – K‑Means Clustering

K‑Means Clustering

K‑Means groups unlabeled data into k clusters by minimizing intra‑cluster variance.

Algorithm steps

1. Randomly initialize k centroids.
2. Assign each point to the nearest centroid.
3. Re‑compute centroids as the mean of assigned points.
4. Iterate steps 2‑3 until convergence.

Using scikit‑learn

from sklearn.cluster import KMeans

kmeans = KMeans(n_clusters=3, random_state=42)
clusters = kmeans.fit_predict(X_scaled)

df['cluster'] = clusters

Elbow method to find optimal k

inertia = []
K = range(1, 11)
for k in K:
    km = KMeans(n_clusters=k, random_state=42)
    km.fit(X_scaled)
    inertia.append(km.inertia_)

plt.plot(K, inertia, 'bo-')
plt.xlabel('Number of clusters k')
plt.ylabel('Inertia (Sum of squared distances)')
plt.title('Elbow Method')
plt.show()

Visualizing clusters (2‑D using PCA)

from sklearn.decomposition import PCA
pca = PCA(n_components=2)
proj = pca.fit_transform(X_scaled)

plt.scatter(proj[:,0], proj[:,1], c=clusters, cmap='viridis', s=50)
plt.title('K‑Means Clusters (PCA projection)')
plt.show()

Silhouette score (cluster quality)

from sklearn.metrics import silhouette_score
score = silhouette_score(X_scaled, clusters)
print('Silhouette Score:', score)

Limitations

• Assumes spherical clusters.
• Sensitive to scaling (hence standardize first).
• Requires pre‑specifying k.