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:

1	`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.

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

Links:

http://scikit-learn.org/stable/modules/generated/sklearn.metrics.fowlkes_mallows_score.html

doc_scikit_learn

2025-01-10 15:47:30

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