The Dunn Index is another measure used to validate the quality of cluster configurations.

It evaluates clustering by identifying compact and well-separated clusters.

The Dunn Index is defined as the ratio of the smallest distance between observations in different clusters to the largest intra-cluster distance. The goal is to maximise the Dunn Index, where higher values indicate better clustering with greater separation between clusters and compactness within clusters.

$$ DI = \min_{1 \leq i \leq k} \left( \min_{1 \leq j \leq k, i \neq j} \left( \frac{\delta(i, j)}{\max_{1 \leq l \leq k} \Delta(l)} \right) \right) $$

Where:

• $δ(i, j)$ (’delta i j’) is the distance between clusters $i$ and $j$, typically measured as the distance between the nearest members of the clusters.
• $Δ(l)$ is the maximum intra-cluster distance in cluster $l$.

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Multiple Regression