Fowlkes–Mallows index

Description

The Fowlkes-Mallows index is an external evaluation method used to determine the similarity between two classifications (clusters). This measure can compare either two hierarchical clusterings or a clustering with a reference classification. This index is particularly useful for evaluating the performance of clustering algorithms. A higher index value indicates greater similarity between the clusters and the reference classifications The index ranges from 0 (worst possible classification) to 1 (perfect classification). It is the geometric mean of precision and recall, making it a robust metric for clustering evaluation.

Formulas

The Fowlkes-Mallows index can be expressed in several ways depending on the context.

General Formulation :

\[ FM=TPTP+FP⋅TPTP+FNFM=\sqrt{\frac{TP}{TP+FP}\cdot\frac{TP}{TP+FN}} \]

where :

  • \(TP\) is the number of True Positives

  • \(FP\) is the number of False Positives

  • \(FN\) is the number of False Negatives

Sources

Wikipedia

E. B. FOWLKES et C. L. MALLOWS. « A method for comparing two hierarchical clusterings ». In : Journal of the American Statistical Association 78 (1983).

“Applying Deep Learning algorithm to perform lung cells annotation”, A. Collin, 2020

Code

Scikit