Dunn index

The Dunn Index (DI) is a metric for judging a clustering algorithm. A higher DI implies better clustering. It assumes that better clustering means that clusters are compact and well-separated from other clusters.

There are many ways to define the size of a cluster and distance between clusters.

The DI is equal to the minimum inter-cluster distance divided by the maximum cluster size. Note that larger inter-cluster distances (better separation) and smaller cluster sizes (more compact clusters) lead to a higher DI value.

In mathematical terms:

Let the size of cluster C be denoted by: ${\mathrm{\Delta }}_C$

Let the distance between clusters i and j be denoted by: $\delta (C_i,C_j)$

$DI=\frac{\min {\mathrm{\backslash limits}}_{1\le i\le j\le m}\delta (C_i,C_j)}{\max {\mathrm{\backslash limits}}_{1\le k\le m}{\mathrm{\Delta }}_k}$