Normalized Mutual Information Calculator
Information shared between two clusterings or label sets, normalized to 0–1 — a chance-aware clustering metric.
NMI measures how much knowing one clustering tells you about the other, scaled to [0,1]. Unlike ARI it handles differing cluster counts gracefully, which is why it's popular for comparing clusterings with different K. Use the adjusted variant (AMI) when chance correction matters most.
Formula
Disclaimer: This tool is for general informational and estimation purposes only and is not professional financial, tax, accounting or legal advice. All figures are estimates — verify with a qualified professional before making decisions. Read the full disclaimer.
About Normalized Mutual Information Calculator
Normalized Mutual Information measures how much two clusterings (or a clustering and ground-truth labels) tell you about each other, using information theory: it computes the mutual information between the two partitions and normalizes by their average entropy so the score lands in [0,1], where 0 means statistically independent and 1 means identical. This calculator takes a contingency matrix of co-occurrence counts and returns both raw mutual information and NMI. Its key advantage over the Adjusted Rand Index is graceful handling of clusterings with different numbers of clusters.
How to use Normalized Mutual Information Calculator
- 1Enter your values into Normalized Mutual Information Calculator — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
- 2The result recomputes live using the formula shown on the page; there is no button to press.
- 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.
Why use Normalized Mutual Information Calculator?
- ✓Computes Normalized Mutual Information instantly in your browser — no sign-up, no upload, no server round-trip.
- ✓100% free and unlimited, with the exact formula shown: NMI = 2.
- ✓Runs entirely client-side, so every value you enter stays private on your device.
- ✓Live recompute as you type, with a worked example and authoritative references for trust.
Frequently asked questions
NMI vs Adjusted Rand Index — which should I use?+
Both are external clustering metrics that usually agree. NMI (information-theoretic) handles differing cluster counts more gracefully and has a clean 0–1 scale; ARI (pair-counting) is more intuitive and explicitly chance-corrected. Use NMI when comparing partitions with very different K; use ARI when you want pair-agreement intuition. Reporting both is common.
Why normalize mutual information?+
Raw mutual information is unbounded and grows with the number of clusters, making it incomparable across different clusterings. Normalizing by the average (or geometric mean, or max) of the two entropies caps it at 1 for identical partitions, giving a standardized score you can compare and average across experiments.
What is Adjusted Mutual Information (AMI)?+
NMI doesn't fully correct for chance — random clusterings with many clusters can score above 0. AMI subtracts the expected mutual information of random partitions, so random labelings score ~0 like ARI does. For rigorous comparison, especially with many clusters, AMI is preferred; NMI remains popular for its simplicity.
Does NMI work with imbalanced cluster sizes?+
It's more robust to imbalance than raw accuracy-style metrics because it's based on information content, but very imbalanced partitions still affect the entropy terms. As with all clustering metrics, inspect the contingency matrix directly alongside the score — a single number never tells the whole story of how two partitions relate.
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