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 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 createdwhere
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