sklearn.metrics
.v_measure_score¶

sklearn.metrics.
v_measure_score
(labels_true, labels_pred, beta=1.0)[source]¶ Vmeasure cluster labeling given a ground truth.
This score is identical to
normalized_mutual_info_score
with the'arithmetic'
option for averaging.The Vmeasure is the harmonic mean between homogeneity and completeness:
v = (1 + beta) * homogeneity * completeness / (beta * homogeneity + completeness)
This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way.
This metric is furthermore symmetric: switching
label_true
withlabel_pred
will return the same score value. This can be useful to measure the agreement of two independent label assignments strategies on the same dataset when the real ground truth is not known.Read more in the User Guide.
Parameters:  labels_true : int array, shape = [n_samples]
ground truth class labels to be used as a reference
 labels_pred : array, shape = [n_samples]
cluster labels to evaluate
 beta : float
Ratio of weight attributed to
homogeneity
vscompleteness
. Ifbeta
is greater than 1,completeness
is weighted more strongly in the calculation. Ifbeta
is less than 1,homogeneity
is weighted more strongly.
Returns:  v_measure : float
score between 0.0 and 1.0. 1.0 stands for perfectly complete labeling
References
[1] Andrew Rosenberg and Julia Hirschberg, 2007. VMeasure: A conditional entropybased external cluster evaluation measure Examples
Perfect labelings are both homogeneous and complete, hence have score 1.0:
>>> from sklearn.metrics.cluster import v_measure_score >>> v_measure_score([0, 0, 1, 1], [0, 0, 1, 1]) 1.0 >>> v_measure_score([0, 0, 1, 1], [1, 1, 0, 0]) 1.0
Labelings that assign all classes members to the same clusters are complete be not homogeneous, hence penalized:
>>> print("%.6f" % v_measure_score([0, 0, 1, 2], [0, 0, 1, 1])) ... 0.8... >>> print("%.6f" % v_measure_score([0, 1, 2, 3], [0, 0, 1, 1])) ... 0.66...
Labelings that have pure clusters with members coming from the same classes are homogeneous but unnecessary splits harms completeness and thus penalize Vmeasure as well:
>>> print("%.6f" % v_measure_score([0, 0, 1, 1], [0, 0, 1, 2])) ... 0.8... >>> print("%.6f" % v_measure_score([0, 0, 1, 1], [0, 1, 2, 3])) ... 0.66...
If classes members are completely split across different clusters, the assignment is totally incomplete, hence the VMeasure is null:
>>> print("%.6f" % v_measure_score([0, 0, 0, 0], [0, 1, 2, 3])) ... 0.0...
Clusters that include samples from totally different classes totally destroy the homogeneity of the labeling, hence:
>>> print("%.6f" % v_measure_score([0, 0, 1, 1], [0, 0, 0, 0])) ... 0.0...