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# `sklearn.metrics`.v_measure_score

sklearn.metrics.v_measure_score(labels_true, labels_pred, *, beta=1.0)

  V-measure cluster labeling given a ground truth.

  This score is identical to `normalized_mutual_info_score` with the `'arithmetic'` option for averaging.

  The V-measure 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` with `label_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 array-like of shape (n_samples,)

      Ground truth class labels to be used as a reference.

    labels_pred array-like of shape (n_samples,)

      Cluster labels to evaluate.

    beta float, default=1.0

      Ratio of weight attributed to `homogeneity` vs `completeness`. If `beta` is greater than 1, `completeness` is weighted more strongly in the calculation. If `beta` 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.

  See also

  `homogeneity_score`

    Homogeneity metric of cluster labeling.

  `completeness_score`

    Completeness metric of cluster labeling.

  `normalized_mutual_info_score`

    Normalized Mutual Information.

  References

  [1]

  Andrew Rosenberg and Julia Hirschberg, 2007. V-Measure: A conditional entropy-based 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 but 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 un-necessary splits harm completeness and thus penalize V-measure 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 V-Measure 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...

## Examples using `sklearn.metrics.v_measure_score`

Release Highlights for scikit-learn 1.3

Release Highlights for scikit-learn 1.3

Biclustering documents with the Spectral Co-clustering algorithm

Biclustering documents with the Spectral Co-clustering algorithm

A demo of K-Means clustering on the handwritten digits data

A demo of K-Means clustering on the handwritten digits data

Adjustment for chance in clustering performance evaluation

Adjustment for chance in clustering performance evaluation

Demo of DBSCAN clustering algorithm

Demo of DBSCAN clustering algorithm

Demo of affinity propagation clustering algorithm

Demo of affinity propagation clustering algorithm

Clustering text documents using k-means

Clustering text documents using k-means