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 other distance measure two items close-by, then the variation of information will also judge them close.
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This is completely equivalent to the shared information distance.
- Alexander Kraskov, Harald Stögbauer, Ralph G. Andrzejak, and Peter Grassberger, "Hierarchical Clustering Based on Mutual Information", (2003) ArXiv q-bio/0311039
- Arabie, P.; Boorman, S. A. (1973). "Multidimensional scaling of measures of distance between partitions". Journal of Mathematical Psychology 10: 148–203.
- Meila, Marina (2003). "Comparing Clusterings by the Variation of Information". Learning Theory and Kernel Machines: 173–187.
- 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.
- Kingsford, Carl (2009). "Information Theory Notes" (PDF). Retrieved 22 September 2009.