Use variation of clustering information to compare pairs of splits

Compare a pair of splits viewed as clusterings of taxa, using the variation of clustering information proposed by Meila2007TreeDist.

Usage

MeilaVariationOfInformation(split1, split2)

MeilaMutualInformation(split1, split2)

Arguments

split1, split2

Logical vectors listing leaves in a consistent order, identifying each leaf as a member of the ingroup (TRUE) or outgroup (FALSE) of the split in question.

Value

MeilaVariationOfInformation() returns the variation of (clustering) information, measured in bits.

MeilaMutualInformation() returns the mutual information, measured in bits.

Details

This is equivalent to the mutual clustering information Vinh2010TreeDist. For the total information content, multiply the VoI by the number of leaves.

References

Author

Martin R. Smith (martin.smith@durham.ac.uk)

Examples

# Maximum variation = information content of each split separately
A <- TRUE
B <- FALSE
MeilaVariationOfInformation(c(A, A, A, B, B, B), c(A, A, A, A, A, A))
#> [1] 1
Entropy(c(3, 3) / 6) + Entropy(c(0, 6) / 6)
#> [1] 1

# Minimum variation = 0
MeilaVariationOfInformation(c(A, A, A, B, B, B), c(A, A, A, B, B, B))
#> [1] 0

# Not always possible for two evenly-sized splits to reach maximum
# variation of information
Entropy(c(3, 3) / 6) * 2  # = 2
#> [1] 2
MeilaVariationOfInformation(c(A, A, A,B ,B, B), c(A, B, A, B, A, B)) # < 2
#> [1] 1.836592

# Phylogenetically uninformative groupings contain spliting information
Entropy(c(1, 5) / 6)
#> [1] 0.6500224
MeilaVariationOfInformation(c(B, A, A, A, A, A), c(A, A, A, A, A, B))
#> [1] 1.203213