AllSplitPairings {TreeDist}

Variation of information for all split pairings

Description

Calculate the variation of clustering information (Meila 2007) for each possible pairing of non-trivial splits on n leaves (Smith 2020), tabulating the number of pairings with each similarity.

Usage

AllSplitPairings(n)

Arguments

n

Integer specifying the number of leaves in a tree.

Value

AllSplitPairings() returns a named vector. The name of each element corresponds to a certain variation of information, in bits; the value of each element specifies the number of pairings of non-trivial splits that give rise to that variation of information. Split AB|CD is treated as distinct from CD|AB. If pairing AB|CD=CD|AB is considered equivalent to CD|AB=CD|AB (etc), then values should be divided by four.

Author(s)

Martin R. Smith ([e-mail])

References

Meila M (2007). “Comparing clusterings—an information based distance.” Journal of Multivariate Analysis, 98(5), 873–895. doi:10.1016/j.jmva.2006.11.013.

Smith MR (2020). “Information theoretic Generalized Robinson-Foulds metrics for comparing phylogenetic trees.” Bioinformatics, 36(20), 5007–5013. doi:10.1093/bioinformatics/btaa614.

Examples

AllSplitPairings(6)
# Treat equivalent splits as identical by dividing by four:
AllSplitPairings(6) / 4L