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Completeness

A ground-truth clustering metric that measures how well all the samples of a class are grouped into a single cluster. A clustering is said to be complete when every sample of a class is contained in one cluster. Formally, it is one minus the conditional entropy of the cluster assignments given the classes normalized by the marginal entropy of the cluster assignments.

\[ {\displaystyle Completeness = 1-\frac{H(K \mid C)}{H(K)}} \]

Assigning every sample its own cluster keeps the clusters perfectly pure (homogeneity 1) but scatters each class across multiple clusters, so completeness is heavily penalized. See V Measure for the balanced combination of homogeneity and completeness, or Class Purity for the purity-based counterpart of this metric.

Note

Since this metric monotonically improves as the number of target clusters decreases, it should not be used as a metric to guide hyper-parameter tuning.

Note

When all samples share a single cluster assignment, completeness is defined as 1 since there is no cluster entropy left to explain. An empty set of predictions scores 0.

Estimator Compatibility: Clusterer

Score Range: 0 to 1

Parameters

This metric does not have any parameters.

Example

use Rubix\ML\CrossValidation\Metrics\Completeness;

$metric = new Completeness();

$score = $metric->score([0, 1, 2, 3, 4], ['lamb', 'lamb', 'wolf', 'wolf', 'wolf']);

echo $score;

0.41816566007905