Dunn Index Calculator

The Dunn Index Calculator measures how well data points are clustered. It checks two things: how far apart different clusters are and how tight each cluster is inside. The result is a number—the Dunn Index—where a higher value means better clustering. Good clustering has clusters that are far from each other and close within themselves.

This calculator helps with real-life decisions, like improving data analysis, testing machine learning models, or organizing information. It’s reliable for important tasks, like ensuring your clusters make sense. Want to know how it’s calculated? Let’s check out the formula next.

Formula for Dunn Index

The formula for finding the Dunn Index is:

Dunn Index = min(δ(Ci, Cj)) / max(Δ(Ck))

Where:

• δ(Ci, Cj) = Inter-cluster distance between clusters Ci and Cj
• Δ(Ck) = Intra-cluster diameter of cluster Ck
• min(δ(Ci, Cj)) = Smallest distance between any two clusters
• max(Δ(Ck)) = Biggest diameter within any cluster

Inter-Cluster Distance

δ(Ci, Cj) = min{d(x, y) | x ∈ Ci, y ∈ Cj}

Where:

• d(x, y) = Distance between points x and y (usually Euclidean distance)

Intra-Cluster Diameter

Δ(Ck) = max{d(x, y) | x, y ∈ Ck}

A higher Dunn Index shows clusters are well-separated and compact. This formula comes from data science research. Now, let’s make it easier with a table.

Quick Reference Table for Dunn Index Values

Why calculate every time? This table explains what Dunn Index values mean. It’s a fast way to understand your results.

Dunn Index Range	Meaning
0.0-0.5	Poor clustering—clusters overlap or spread out
0.5-1.0	Okay clustering—some separation, decent fit
1.0+	Good clustering—clear, tight groups

How to Use the Table

• Find your Dunn Index value.
• Check what it says about your clusters.
• Use it to improve your work.

This table helps with searches like “what’s a good Dunn Index.” For exact results, use the formula. Next, let’s try an example.

Example of Dunn Index Calculator

Suppose you have three clusters with these points (using simple 2D coordinates):

• Cluster 1: (1,1), (2,2)
• Cluster 2: (5,5), (6,6)
• Cluster 3: (9,9), (10,10)

1. Calculate intra-cluster diameters (max distance within each):
   • Cluster 1: d((1,1), (2,2)) = √2 ≈ 1.41
   • Cluster 2: d((5,5), (6,6)) = √2 ≈ 1.41
   • Cluster 3: d((9,9), (10,10)) = √2 ≈ 1.41
   • max(Δ(Ck)) = 1.41
2. Calculate inter-cluster distances (min between clusters):
   • C1 to C2: d((2,2), (5,5)) = √18 ≈ 4.24
   • C1 to C3: d((2,2), (9,9)) = √98 ≈ 9.90
   • C2 to C3: d((6,6), (9,9)) = √18 ≈ 4.24
   • min(δ(Ci, Cj)) = 4.24
3. Plug into the formula:
   Dunn Index = 4.24 / 1.41 ≈ 3.01

So, the Dunn Index is about 3.01—showing good clustering with tight, far-apart groups.

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