# Purity¶

Purity.

In a similar fashion with Entropy, the purity of a clustering solution, compared to the original true label is defined to be the fraction of the overall cluster size that the largest class of documents assigned to that cluster represents. The overall purity of the clustering solution is obtained as a weighted sum of the individual cluster purities and is given by:

$Purity = \sum_{r=1}^k \frac{n_r}{n} \times \left( \frac{1}{n_r} \max_i (n^i_r) \right) = \sum_{r=1}^k \frac{1}{n} \max_i (n^i_r)$

## 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.Purity()
>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp).get())
1.0
1.0
0.6666666666666666
0.75
0.6
0.6666666666666666

>>> metric
Purity: 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.

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. Ying Zhao and George Karypis. 2001. Criterion functions for ducument clustering: Experiments and analysis. Technical Report TR 01–40, Department of Computer Science, University of Minnesota.