Evaluation: Silhouette Score, Elbow Method

Silhouette Score

The Silhouette Score measures how similar a data point is to its own cluster compared to other clusters. It ranges from -1 to 1:

• +1: Perfectly matched to its own cluster, and far from others
• 0: On or very close to the decision boundary between two clusters
• -1: Probably assigned to the wrong cluster

A higher average silhouette score indicates better-defined clusters.

Elbow Method

The Elbow Method helps determine the optimal number of clusters by plotting the within-cluster sum of squares (WCSS) against the number of clusters.

• As the number of clusters increases, WCSS decreases
• The point where the WCSS curve starts to flatten is considered the "elbow," indicating the optimal cluster count

This method is most effective when the data exhibits a clear elbow shape in the plot.

Python Example: Silhouette Score & Elbow Method

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

# Create sample data
X, _ = make_blobs(n_samples=300, centers=4, random_state=42)

# Elbow Method
wcss = []
for i in range(1, 11):
    kmeans = KMeans(n_clusters=i, random_state=42)
    kmeans.fit(X)
    wcss.append(kmeans.inertia_)

plt.plot(range(1, 11), wcss, marker='o')
plt.title('Elbow Method')
plt.xlabel('Number of clusters')
plt.ylabel('WCSS')
plt.show()

# Silhouette Score for 4 clusters
kmeans = KMeans(n_clusters=4, random_state=42)
labels = kmeans.fit_predict(X)
score = silhouette_score(X, labels)
print(f'Silhouette Score: {score:.2f}')