
Fowlkes–Mallows Index
Encyclopedia
Fowlkes-Mallows index is an external evaluation method that used to determine the similarity between two clusterings (clusters obtained after a clustering algorithm). This measure of similarity could be either between two hierarchical clusterings or a clustering and a benchmark classification.
The higher the value of the Fowlkes-Mallows index the more similar the clusters and the benchmark classifications are.
objects labeled
and
. The trees
and
can be cut to produce
clusters for each tree (by either selecting clusters at a particular height of the tree or setting different strength of the hierarchical clustering). For each value of
, the following table can then be created

where
is of objects common between the
th cluster of
and
th cluster
. The Fowlkes-Mallows index for the specific value of
is then defined as
where

The higher the value of the Fowlkes-Mallows index the more similar the clusters and the benchmark classifications are.
Preliminaries
The Fowlkes-Mallows index, when results of two clustering algorithms are used to evaluate the results of a clustering algorithm, is defined as
- where
is the number of true positives,
is the number of false positives, and
is the number of false negatives.
Definition
Consider two hierarchical clusterings of







where






where


