# NormalizedMutualInfo¶

Normalized Mutual Information between two clusterings.

Normalized Mutual Information (NMI) is a normalized version of the Mutual Information (MI) score to scale the results between the range of 0 (no mutual information) and 1 (perfectly mutual information). In the formula, the mutual information will be normalized by a generalized mean of the entropy of true and predicted labels, defined by the average_method.

We note that this measure is not adjusted for chance (i.e corrected the effect of result agreement solely due to chance); as a result, the Adjusted Mutual Info Score will mostly be preferred. However, this metric is still symmetric, which means that switching true and predicted labels will not alter the score value. This fact can be useful when the metric is used to measure the agreement between two indepedent label solutions on the same dataset, when the ground truth remains unknown.

Another advantage of the metric is that as it is based on the calculation of entropy-related measures, it is independent of the permutation of class/cluster labels.

## Parameters¶

• 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.

• average_method – defaults to arithmetic

This parameter defines how to compute the normalizer in the denominator. Possible options include min, max, arithmetic and geometric.

## Attributes¶

• 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

## Examples¶

>>> from river import metrics

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

>>> metric = metrics.NormalizedMutualInfo()
>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp).get())
1.0
1.0
0.0
0.343711
0.458065
0.515803

>>> metric
NormalizedMutualInfo: 0.515804


## Methods¶

clone

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.

get

Return the current value of the metric.

is_better_than
revert

Revert the metric.

Parameters

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

Update the metric.

Parameters

• y_true
• y_pred
• sample_weight – defaults to 1.0
works_with

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

Parameters

• model (river.base.estimator.Estimator)

## References¶

1. Wikipedia contributors. (2021, March 17). Mutual information. In Wikipedia, The Free Encyclopedia, from https://en.wikipedia.org/w/index.php?title=Mutual_information&oldid=1012714929