Dunn index

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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:

Let the distance between clusters i and j be denoted by: