Dunn Index

The Dunn Index is defined as:

$D=\frac{{\min }_{1\le i<j\le K}\delta \left(C_i,C_j\right)}{{\max }_{1\le k\le K}{\delta }^{\prime }\left(C_k\right)}$

Where:

• $K$ is the number of clusters;
• $\delta (C_i,C_j)$ is the distance between the centroids of cluster $C_i$ and $C_j$;
• ${\delta }^{\prime }(C_k)$ is the intra-cluster distance of cluster $C_k$, that is defined as the $\max$ (or $\text{avg}$) distance between each pair of objects in the cluster.

The idea is here to minimize the inter-class distance on the numerator and maximise the intra-class distance on the denominator.

The higher the index, the better.

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clustering