# Completeness¶

Completeness Score.

Completeness 1 is symmetrical to homogeneity. In order to satisfy the completeness criteria, a clustering must assign all of those datapoints that are members of a single class to a single cluster. To evaluate completeness, we examine the distribution cluster assignments within each class. In a perfectly complete clustering solution, each of these distributions will be completely skewed to a single cluster.

We can evaluate this degree of skew by calculating the conditional entropy of the proposed cluster distribution given the class of the component data points. However, in the worst case scenario, each class is represented by every cluster with a distribution equal to the distribution of cluster sizes. Therefore, symmetric to the claculation above, we define completeness as:

$c = \begin{cases} 1 if H(K) = 0, \\ 1 - \frac{H(K|C)}{H(K)} otherwise. \end{cases}.$

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

>>> metric = metrics.Completeness()
>>> for yt, yp in zip(y_true, y_pred):
...     print(metric.update(yt, yp).get())
1.0
1.0
1.0
0.3836885465963443
0.5880325916843805
0.6666666666666667

>>> metric
Completeness: 66.67%


## 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)

1. Andrew Rosenberg and Julia Hirschberg (2007). V-Measure: A conditional entropy-based external cluster evaluation measure. Proceedings of the 2007 Joing Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pp. 410 - 420, Prague, June 2007.