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Mutual Information between two clusterings.

The Mutual Information 1 is a measure of the similarity between two labels of the same data. Where \(|U_i|\) is the number of samples in cluster \(U_i\) and \(|V_j|\) is the number of the samples in cluster \(V_j\), the Mutual Information between clusterings \(U\) and \(V\) can be calculated as:

\[ MI(U,V) = \sum_{i=1}^{|U|} \sum_{v=1}^{|V|} \frac{|U_i \cup V_j|}{N} \log \frac{N |U_i \cup V_j|}{|U_i| |V_j|} \]

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.

This metric is furthermore symmetric: switching y_true and y_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.

The Mutual Information can be equivalently expressed as:

\[ MI(U,V) = H(U) - H(U | V) = H(V) - H(V | U) \]

where \(H(U)\) and \(H(V)\) are the marginal entropies, \(H(U | V)\) and \(H(V | U)\) are the conditional entropies.


  • cm – defaults to None

    This parameter allows sharing the same confusion matrix between multiple metrics. Sharing a confusion matrix reduces the amount of storage and computation time.


  • bigger_is_better

    Indicate if a high value is better than a low one or not.

  • requires_labels

    Indicates if labels are required, rather than probabilities.

  • sample_correction

  • works_with_weights

    Indicate whether the model takes into consideration the effect of sample weights


>>> from river import metrics

>>> y_true = [1, 1, 2, 2, 3, 3]
>>> y_pred = [1, 1, 1, 2, 2, 2]

>>> metric = metrics.MutualInfo()
>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp).get())

>>> metric
MutualInfo: 0.462098



Return a fresh estimator with the same parameters.

The clone has the same parameters but has not been updated with any data. This works by looking at the parameters from the class signature. Each parameter is either - recursively cloned if it's a River classes. - deep-copied via copy.deepcopy if not. If the calling object is stochastic (i.e. it accepts a seed parameter) and has not been seeded, then the clone will not be idempotent. Indeed, this method's purpose if simply to return a new instance with the same input parameters.


Return the current value of the metric.


Revert the metric.


  • y_true
  • y_pred
  • sample_weight – defaults to 1.0
  • correction – defaults to None

Update the metric.


  • y_true
  • y_pred
  • sample_weight – defaults to 1.0

Indicates whether or not a metric can work with a given model.


  • model (river.base.estimator.Estimator)


  1. Wikipedia contributors. (2021, March 17). Mutual information. In Wikipedia, The Free Encyclopedia, from