## What is the Fowlkes-Mallows Index?

The **Fowlkes-Mallows Index** (FMI, Fowlkes-Mallows Score or G-Mean) is a performance metric to evaluate the similarity of clusters obtained through various clustering algorithms. It is typically used to evaluate the clustering performance of a specific algorithm by assuming that the cluster it is compared to is the ground truth — i.e. the perfect cluster.

With this in mind, one can easily grasp how it is also a valid (external) measure for evaluating supervised learning algorithms. The FMI is defined as the geometric mean of the pairwise precision and recall.

FM = \sqrt{ PPV \cdot TPR} = \sqrt{ \frac {TP}{TP+FP} \cdot \frac{TP}{TP+FN} }

The FMI has several advantages:

- With a random classification, the FMI will approach zero.
- The FMI is upper-bound. A perfect classification will result in an FMI of 1.

Further reading: