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Homogeneity

A ground-truth clustering metric that measures how well each cluster is comprised of samples from a single class. A clustering is said to be homogeneous when all of its clusters contain only samples of a single class. Formally, it is one minus the conditional entropy of the classes given the cluster assignments normalized by the marginal entropy of the classes.

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

Even though each cluster contains a majority of samples from a single class, both clusters mix classes and the score is close to zero. A clustering is homogeneous only when every cluster contains samples from exactly one class. See V Measure for the balanced combination of homogeneity and completeness, or Cluster Purity for the purity-based counterpart of this metric.

Note

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

Note

When the ground-truth contains only one class, homogeneity is defined as 1 since there is no class 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\Homogeneity;

$metric = new Homogeneity();

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

echo $score;

0.020570659450693