Adjusted Mutual Information between two clusterings.

Adjusted Mutual Information (AMI) is an adjustment of the Mutual Information score that accounts for chance. It corrects the effect of agreement solely due to chance between clusterings, similar to the way the Adjusted Rand Index corrects the Rand Index. It is closely related to variation of information. The adjusted measure, however, is no longer metrical.

For two clusterings $$U$$ and $$V$$, the Adjusted Mutual Information is calculated as:

$AMI(U, V) = \frac{MI(U, V) - E(MI(U, V))}{avg(H(U), H(V)) - E(MI(U, V))}$

This metric is independent of the permutation of the class or cluster label values; furthermore, it is also symmetric. This can be useful to measure the agreement of two label assignments strategies on the same dataset, regardless of the ground truth.

However, due to the complexity of the Expected Mutual Info Score, the computation of this metric is an order of magnitude slower than most other metrics, in general.

## Parameters¶

• cm

DefaultNone

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

Defaultarithmetic

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.

• 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]

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

1.0
1.0
0.0
0.0
0.105891
0.298792


metric

AdjustedMutualInfo: 0.298792


## Methods¶

get

Return the current value of the metric.

is_better_than

Indicate if the current metric is better than another one.

Parameters

• other

revert

Revert the metric.

Parameters

• y_true
• y_pred
• sample_weight — defaults to 1.0

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

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