Characterization of the Jaccard dissimilarity metric and a generalization.

The Jaccard dissimilarity metric identifies the distance between two finite sets by the number of their unique elements as a proportion of their joint cardinality. This note gives an elementary characterization of the Jaccard metric by means of three simple axioms. Relaxing the most substantial one allows for a general family of new dissimilarity quasi-metrics to emerge that encompasses Jaccard's metric. [ABSTRACT FROM AUTHOR]