Understanding the Silhouette Score

Introduction

Clustering is a cornerstone of unsupervised machine learning, and assessing the quality of clustering is crucial. One effective method for evaluating clustering algorithms is the Silhouette Score. This metric helps in determining the separation distance between the resulting clusters. Understanding this score is key to enhancing the effectiveness of cluster analysis.

What is the Silhouette Score?

The Silhouette Score is a measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation). The silhouette ranges from -1 to +1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. If most objects have a high value, then the clustering configuration is appropriate. If many points have a low or negative value, then the clustering configuration may have too many or too few clusters.

The Mathematics Behind the Silhouette Score

The Silhouette Score for each point is calculated using the following formula:

• a(i): The average distance from the ith point to the other points in the same cluster.
• b(i): The minimum average distance from the ith point to points in a different cluster, minimized over clusters.

When to Use Silhouette Score