Clustering metrics

Sources:

• K-Means Clustering: From A to Z (Towards Data Science)

• Clustering performance evaluation (Scikit Learn)

• The Silhouette Loss Function: Metric Learning with a Cluster Validity Index

• ML | Inter-cluster and Intra-cluster distances (Geeks for Geeks)

Theses metrics evaluate how good is the clustering structure with no need for external information. Clustering evaluation metrics may belong to one of these types:

• Intercluster distance

• Intracluster distance

• Hybrid (combines both)

Inertia

• Or within-cluster sum-of-squares criterion.

• Tells how far away the points within a cluster are.

• The range of the score is: $[0, +\infty )$. So, the lowest is better.

$$\sum_{i=0}^{n}\min_{\mu_j \in C}(||x_i - \mu_j||^2) \\ \text{where } \mu_j \text{ is the centroid of each cluster and } x_i \text{ a data point.}$$

Silhouette score

• It give information about the inter-cluster distances and the intra-cluster distances.

• Tells how far away the instances in one cluster are, from the instances of another cluster.

• The range of the score is $[ -1, 1]$. The highest is better.