Entropy of two splits

Calculate the entropy, joint entropy, entropy distance and information content of two splits, treating each split as a division of n leaves into two groups. Further details are available in a vignette, MacKay (2003) and Meila (2007) .

Usage

SplitEntropy(split1, split2 = split1)

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

A numeric vector listing, in bits:

• H1 The entropy of split 1;

• H2 The entropy of split 2;

• H12 The joint entropy of both splits;

• I The mutual information of the splits;

• Hd The entropy distance (variation of information) of the splits.

References

MacKay DJC (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press, Cambridge. https://www.inference.org.uk/itprnn/book.pdf.

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 .

See also

Other information functions: SplitSharedInformation(), TreeInfo

Author

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

Examples

A <- TRUE
B <- FALSE
SplitEntropy(c(A, A, A, B, B, B), c(A, A, B, B, B, B))
#>        H1        H2       H12         I        Hd 
#> 1.0000000 0.9182958 1.4591479 0.4591479 1.0000000