The V-Measure is defined as the harmonic mean of homogeneity h and completeness c of the clustering. Both these measures can be expressed in terms of the mutual information and entropy measures of the information theory.

V_\beta = (1+\beta)\frac{h \cdot c}{\beta \cdot h + c}

Homogeneity h is maximized when each cluster contains elements of as few different classes as possible. Completeness c aims to put all elements of each class in single clusters.


Andrew Rosenberg and Julia Hirschberg, 2007. “V-Measure: A conditional entropy-based external cluster evaluation measure”

The metric is implemented by the vmeasure function:

vmeasure(assign1, assign2; β = 1.0)

Compute V-measure value between two clustering assignments.

  • assign1 – the vector of assignments for the first clustering.
  • assign2 – the vector of assignments for the second clustering.
  • β – the weight of harmonic mean of homogeneity and completeness.

a V-measure value.

vmeasure(R, assign)

This method takes R, an instance of ClusteringResult, and the corresponding assignment vector assign as input, and computes V-measure value (see above).

vmeasure(R1, R2)

This method takes R1 and R2 (both are instances of ClusteringResult) and computes V-measure value (see above).

It is equivalent to vmeasure(assignments(R1), assignments(R1)).