v_measure: V-measure Between Clusterings

Description

Computes the V-measure between two clusterings, such as a predicted and ground truth clustering.

Usage

v_measure(true, pred, beta = 1)

Arguments

true: ground truth clustering represented as a membership vector. Each entry corresponds to an element and the value identifies the assigned cluster. The specific values of the cluster identifiers are arbitrary.
pred: predicted clustering represented as a membership vector.
beta: non-negative weight. A value of 0 assigns no weight to completeness (i.e. the measure reduces to homogeneity), while larger values assign increasing weight to completeness. A value of 1 weights completeness and homogeneity equally.

Details

V-measure is defined as the $\beta$-weighted harmonic mean of homogeneity $h$ and completeness $c$: $$(1 + \beta)\frac{h \cdot c}{\beta \cdot h + c}.$$ The range of V-measure is between 0 and 1, where 1 corresponds to a perfect match between the clusterings. It is equivalent to the normalised mutual information, when the aggregation function is the arithmetic mean.

References

Rosenberg, A. and Hirschberg, J. "V-measure: A conditional entropy-based external cluster evaluation measure." Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), (2007).

Becker, H. "Identification and characterization of events in social media." PhD dissertation, Columbia University, (2011).

Examples

Run this code

true <- c(1,1,1,2,2)  # ground truth clustering
pred <- c(1,1,2,2,2)  # predicted clustering
v_measure(true, pred)