Calculate the variation of clustering information (Meilă 2007) for each possible pairing of non-trivial splits on n leaves, tabulating the number of pairings with each similarity.
AllSplitPairings(n)Integer specifying the number of leaves in a tree.
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.
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 .
AllSplitPairings(6)
#> 0 1 1.33333333333333 1.74837083261218
#> 100 480 360 480
#> 1.83659166810898 1.91829583405449
#> 360 720
# Treat equivalent splits as identical by dividing by four:
AllSplitPairings(6) / 4L
#> 0 1 1.33333333333333 1.74837083261218
#> 25 120 90 120
#> 1.83659166810898 1.91829583405449
#> 90 180