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# `sklearn.metrics`.adjusted_rand_score

sklearn.metrics.adjusted_rand_score(labels_true, labels_pred)

  Rand index adjusted for chance.

  The Rand Index computes a similarity measure between two clusterings by considering all pairs of samples and counting pairs that are assigned in the same or different clusters in the predicted and true clusterings.

  The raw RI score is then “adjusted for chance” into the ARI score using the following scheme:

      ARI = (RI - Expected_RI) / (max(RI) - Expected_RI)

  The adjusted Rand index is thus ensured to have a value close to 0.0 for random labeling independently of the number of clusters and samples and exactly 1.0 when the clusterings are identical (up to a permutation). The adjusted Rand index is bounded below by -0.5 for especially discordant clusterings.

  ARI is a symmetric measure:

      adjusted_rand_score(a, b) == adjusted_rand_score(b, a)

  Read more in the User Guide.

  Parameters:
    labels_true array-like of shape (n_samples,), dtype=int

      Ground truth class labels to be used as a reference.

    labels_pred array-like of shape (n_samples,), dtype=int

      Cluster labels to evaluate.

  Returns:
    ARI float

      Similarity score between -0.5 and 1.0. Random labelings have an ARI close to 0.0. 1.0 stands for perfect match.

  See also

  `adjusted_mutual_info_score`

    Adjusted Mutual Information.

  References

  [Hubert1985]

  L. Hubert and P. Arabie, Comparing Partitions, Journal of Classification 1985 https://link.springer.com/article/10.1007%2FBF01908075

  [Steinley2004]

  D. Steinley, Properties of the Hubert-Arabie adjusted Rand index, Psychological Methods 2004

  [wk]

  https://en.wikipedia.org/wiki/Rand_index#Adjusted_Rand_index

  [Chacon]

  Minimum adjusted Rand index for two clusterings of a given size, 2022, J. E. Chacón and A. I. Rastrojo

  Examples

  Perfectly matching labelings have a score of 1 even

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

  Labelings that assign all classes members to the same clusters are complete but may not always be pure, hence penalized:

      >>> adjusted_rand_score([0, 0, 1, 2], [0, 0, 1, 1])
      0.57...

  ARI is symmetric, so labelings that have pure clusters with members coming from the same classes but unnecessary splits are penalized:

      >>> adjusted_rand_score([0, 0, 1, 1], [0, 0, 1, 2])
      0.57...

  If classes members are completely split across different clusters, the assignment is totally incomplete, hence the ARI is very low:

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

  ARI may take a negative value for especially discordant labelings that are a worse choice than the expected value of random labels:

      >>> adjusted_rand_score([0, 0, 1, 1], [0, 1, 0, 1])
      -0.5

## Examples using `sklearn.metrics.adjusted_rand_score`

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