V-measure¶

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.

References:

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.

Parameters:	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.
Returns:	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)).