sklearn.metrics.fowlkes_mallows_score

sklearn.metrics.fowlkes_mallows_score(labels_true, labels_pred, sparse=False)[source]

Measure the similarity of two clusterings of a set of points.

The Fowlkes-Mallows index (FMI) is defined as the geometric mean between of the precision and recall:

FMI = TP / sqrt((TP + FP) * (TP + FN))

Where TP is the number of True Positive (i.e. the number of pair of points that belongs in the same clusters in both labels_true and labels_pred), FP is the number of False Positive (i.e. the number of pair of points that belongs in the same clusters in labels_true and not in labels_pred) and FN is the number of False Negative (i.e the number of pair of points that belongs in the same clusters in labels_pred and not in labels_True).

The score ranges from 0 to 1. A high value indicates a good similarity between two clusters.

Read more in the User Guide.

Parameters:

labels_true : int array, shape = (n_samples,)

A clustering of the data into disjoint subsets.

labels_pred : array, shape = (n_samples, )

A clustering of the data into disjoint subsets.
Returns:

score : float

The resulting Fowlkes-Mallows score.

References

[R208]E. B. Fowkles and C. L. Mallows, 1983. “A method for comparing two hierarchical clusterings”. Journal of the American Statistical Association
[R209]Wikipedia entry for the Fowlkes-Mallows Index

Examples

Perfect labelings are both homogeneous and complete, hence have score 1.0:

>>> from sklearn.metrics.cluster import fowlkes_mallows_score
>>> fowlkes_mallows_score([0, 0, 1, 1], [0, 0, 1, 1])
1.0
>>> fowlkes_mallows_score([0, 0, 1, 1], [1, 1, 0, 0])
1.0

If classes members are completely split across different clusters, the assignment is totally random, hence the FMI is null:

>>> fowlkes_mallows_score([0, 0, 0, 0], [0, 1, 2, 3])
0.0