Variation of information
Encyclopedia
The variation of information (
) is a measure of the distance between two clusterings (partitions of elements
).
s)
and 
where 
, 
, 
. Then the variation of information between two clusterings is:
where
is entropy of 
and 
is mutual information
between
and 
.
This is completely equivalent to the shared information distance.
) is a measure of the distance between two clusterings (partitions of elementsPartition of a set
In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X...
).
Definition
Suppose we have two clusterings (a division of a set into several subsetSubset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
s)
and where , , . Then the variation of information between two clusterings is:where
is entropy of and is mutual informationMutual information
In probability theory and information theory, the mutual information of two random variables is a quantity that measures the mutual dependence of the two random variables...
between
and .This is completely equivalent to the shared information distance.