Cluster Validity Indices - tahiri-lab/KMeansPhyloTreesClustering GitHub Wiki

📊 Cluster Validity Indices (CH and BH)

In clustering, selecting the optimal number of clusters (K) is a critical step.

K-means requires a predefined number of clusters, but the correct value of K is usually unknown.

To solve this problem, cluster validity indices are used.

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🔹 Calinski-Harabasz Index (CH)

The Calinski-Harabasz index evaluates clustering quality based on:

• Separation between clusters
• Compactness within clusters

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Objective

Maximize:

Between-cluster variance / Within-cluster variance

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Interpretation

• Higher CH value → better clustering
• Indicates well-separated and compact clusters

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🔹 Ball-Hall Index (BH)

The Ball-Hall index focuses on:

• Compactness of clusters

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Objective

Minimize:

• Average variance within clusters

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Interpretation

• Lower BH value → better clustering
• Indicates tight and homogeneous clusters

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🌳 CH and BH in This Project

In this project:

1. K-means is executed for multiple values of K (from Kmin to Kmax)
2. For each K, CH and BH indices are computed
3. The optimal number of clusters is selected based on these indices

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🎯 Role in the Workflow

CH and BH allow:

• Automatic selection of the best number of clusters
• Avoiding arbitrary choice of K
• Improving the reliability of clustering results

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