# Rand¶

Rand Index.

The Rand Index 1 2 is a measure of the similarity between two data clusterings. Given a set of elements S and two partitions of S to compare, X and Y, define the following:

• a, the number of pairs of elements in S that are in the same subset in X and in the same subset in Y

• b, the number of pairs of elements in S that are in the different subset in X and in different subsets in Y

• c, the number of pairs of elements in S that are in the same subset in X and in different subsets in Y

• d, the number of pairs of elements in S that are in the different subset in X and in the same subset in Y

The Rand index, R, is

$R = rac{a+b}{a+b+c+d} = rac{a+b}{ rac{n(n-1)}{2}}.$

## Parameters¶

• cm (river.metrics.confusion.ConfusionMatrix) – 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.

## 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 = [0, 0, 0, 1, 1, 1]
>>> y_pred = [0, 0, 1, 1, 2, 2]

>>> metric = metrics.Rand()

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

>>> metric
Rand: 0.666667


## Methods¶

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
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, January 13). Rand index. In Wikipedia, The Free Encyclopedia, from https://en.wikipedia.org/w/index.php?title=Rand_index&oldid=1000098911

2. W. M. Rand (1971). "Objective criteria for the evaluation of clustering methods". Journal of the American Statistical Association. American Statistical Association. 66 (336): 846–850. arXiv:1704.01036. doi:10.2307/2284239. JSTOR 2284239.