Measure of distance between two clusterings related to mutual 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.[1][2][3]
Information diagram illustrating the relation between information entropies, mutual information and variation of information.
^P. Arabie, S.A. Boorman, S. A., "Multidimensional scaling of measures of distance between partitions", Journal of Mathematical Psychology (1973), vol. 10, 2, pp. 148–203, doi: 10.1016/0022-2496(73)90012-6
^W.H. Zurek, Nature, vol 341, p119 (1989); W.H. Zurek, Physics Review A, vol 40, p. 4731 (1989)
^Marina Meila, "Comparing Clusterings by the Variation of Information", Learning Theory and Kernel Machines (2003), vol. 2777, pp. 173–187, doi:10.1007/978-3-540-45167-9_14, Lecture Notes in Computer Science, ISBN 978-3-540-40720-1
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