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 Meilă (2007).
SplitEntropy(split1, split2 = split1)
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.
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.
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 .