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Matthews correlation coefficient.

The Matthews correlation coefficient (MCC) or phi coefficient is used in Machine Learning as a measure of the quality of classifications, introduced by Brian W. Matthews in 1975. The MCC is defined identically to Pearson's phi coefficient, introduced by Karl Pearson, also known as the Yule phi coefficient from its introduction by Udny Yule in 1912.

The coefficient takes into account true and false positives and negatives and is generally regarded as a balanced measure which can be used even if the classes are of very different sizes. It returns a value between -1 and 1, with 1 being a perfect prediction, 0 no better than random prediction and -1 means a total disagreement between prediction and observation.

The MCC can be calculated directly from the (pair) confusion matrix using the original formula by Matthews. Let

\[ \begin{cases} N = TN + TP + FN + FP = \frac{n(n-1)}{2}, \\ S = \frac{TP + FN}{N}, \\ P = \frac{TP + FP}{N}. \end{cases} \]

The MCC would be then equal to

\[ MCC = \frac{TP / N - S \times P}{\sqrt{PS(1 - S)(1 - P)}}. \]


  • 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.MatthewsCorrCoef()

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

>>> metric
MatthewsCorrCoef: 0.288675



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 26). Matthews correlation coefficient. In Wikipedia, The Free Encyclopedia, from 

  2. Jurman, G., Riccadonna, S., & Furlanello, C. (2012). A Comparison of MCC and CEN Error Measures in Multi-Class Prediction. Plos ONE, 7(8), e41882. doi: 10.1371/journal.pone.0041882