Enter the distances between clusters and the distances between data points within the same cluster into the calculator to determine the Dunn Index.

Use global extrema in the same distance units.

Compare results only for the same data, scaling, distance and definitions. No universal quality cutoff applies.

Related Calculators

Dunn Index Formula

The following formula is used to calculate the Dunn Index.

DI = (global minimum intercluster distance) / (global maximum intracluster diameter)

Variables:

  • DI is the Dunn Index; d(i, j) is the minimum point-to-point distance between clusters i and j
  • d(k, l) is the distance between data points k and l within the same cluster

For standard Dunn, divide the global minimum distance between points in different clusters by the global maximum pairwise distance within any cluster. Compare ratios only for the same data, scaling and distance definition; a larger value describes greater separation relative to spread, not a universal guarantee of clustering quality.

What is a Dunn Index?

The Dunn Index is a metric used in data analysis for determining the compactness and separation of clusters in a data set. It calculates the ratio of the smallest distance between observations not in the same cluster to the largest intra-cluster distance. A higher Dunn Index indicates better clustering, as it signifies that clusters are compact (observations within the same cluster are close to each other) and well-separated (observations in different clusters are far apart).

How to Calculate Dunn Index?

The following steps outline how to calculate the Dunn Index.

  1. First, determine the distance between clusters i and j (d(i, j)).
  2. Next, determine the distance between data points k and l within the same cluster (d(k, l)).
  3. Next, find the maximum value of d(k, l) among all data points within the same cluster.
  4. Next, find the minimum value of d(i, j) among all pairs of clusters.
  5. Finally, calculate the Dunn Index using the formula DI = (global minimum intercluster distance) / (global maximum intracluster diameter).

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Global minimum intercluster distance = 5

Global maximum intracluster diameter = 2; Dunn Index = 5 / 2 = 2.5