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V Measure

V Measure is an entropy-based clustering metric that balances Homogeneity and Completeness. It has the additional property of being symmetric in that the predictions and ground-truth can be swapped without changing the score when beta is left at its default value of 1.

\[ {\displaystyle V_{\beta} = \frac{(1+\beta)hc}{\beta h + c}} \]

Note

A beta greater than 1 gives more weight to homogeneity while a beta less than 1 favors completeness. Since V Measure is a harmonic mean, the score is 0 whenever either homogeneity or completeness is 0.

Note

Unlike Homogeneity and Completeness on their own, V Measure can be used to guide hyper-parameter tuning and is the default scoring metric chosen by Grid Search for clusterers.

Estimator Compatibility: Clusterer

Score Range: 0 to 1

Parameters

#	Name	Default	Type	Description
1	beta	1.0	float	The ratio of weight given to homogeneity over completeness.

Example

use Rubix\ML\CrossValidation\Metrics\VMeasure;

$metric = new VMeasure(1.0);

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

echo $score;

0.020570659450693

References

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1. A. Rosenberg et al. (2007). V-Measure: A conditional entropy-based external cluster evaluation measure. ↩