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 (1) size of a cluster and (2) 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: [math]\displaystyle{ \Delta_C }[/math]

Let the distance between clusters i and j be denoted by: [math]\displaystyle{ \delta(C_i, C_j) }[/math]

[math]\displaystyle{ DI = \frac{\min\limits_{1 \leq i\leq j \leq m} \delta(C_i,C_j)}{\max\limits_{1 \leq k \leq m} \Delta_k} }[/math]