# 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 – 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.

• 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.Rand()

>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp).get())
1.0
1.0
0.3333333333333333
0.5
0.6
0.6666666666666666

>>> metric
Rand: 0.666667


## 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.

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)

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.