Variation of information
In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true metric, in that it obeys the triangle inequality. Even more, it is a universal metric, in that if any[dubious ] other distance measure two items close-by, then the variation of information will also judge them close.
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This is equivalent to the shared information distance between the random variables i and j with respect to the uniform probability measure on defined by for . The variation of information satisfies
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