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# `sklearn.metrics`.homogeneity_completeness_v_measure

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

  Compute the homogeneity and completeness and V-Measure scores at once.

  Those metrics are based on normalized conditional entropy measures of the clustering labeling to evaluate given the knowledge of a Ground Truth class labels of the same samples.

  A clustering result satisfies homogeneity if all of its clusters contain only data points which are members of a single class.

  A clustering result satisfies completeness if all the data points that are members of a given class are elements of the same cluster.

  Both scores have positive values between 0.0 and 1.0, larger values being desirable.

  Those 3 metrics are independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score values in any way.

  V-Measure is furthermore symmetric: swapping `labels_true` and `label_pred` will give the same score. This does not hold for homogeneity and completeness. V-Measure is identical to `normalized_mutual_info_score` with the arithmetic averaging method.

  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,)

      Gluster 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:
    homogeneity float

      Score between 0.0 and 1.0. 1.0 stands for perfectly homogeneous labeling.

    completeness float

      Score between 0.0 and 1.0. 1.0 stands for perfectly complete labeling.

    v_measure float

      Harmonic mean of the first two.

  See also

  `homogeneity_score`

    Homogeneity metric of cluster labeling.

  `completeness_score`

    Completeness metric of cluster labeling.

  `v_measure_score`

    V-Measure (NMI with arithmetic mean option).