Dual total correlation
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(February 2012) ( 
In information theory, dual total correlation (Han 1978), excess entropy (Olbrich 2008), or binding information (Abdallah and Plumbley 2010) is one of the two known nonnegative generalizations of mutual information. While total correlation is bounded by the sum entropies of the n elements, the dual total correlation is bounded by the jointentropy of the n elements. Although well behaved, dual total correlation has received much less attention than the total correlation. A measure known as "TSEcomplexity" defines a continuum between the total correlation and dual total correlation (Ay 2001).
Contents
Definition
For a set of n random variables , the dual total correlation is given by
where is the joint entropy of the variable set and is the conditional entropy of variable , given the rest.
Normalized
The dual total correlation normalized between [0,1] is simply the dual total correlation divided by its maximum value ,
Bounds
Dual total correlation is nonnegative and bounded above by the joint entropy .
Secondly, Dual total correlation has a close relationship with total correlation, . In particular,
Relation to other quantities
In measure theoretic terms, by the definition of dual total correlation:
which is equal to the union of the pairwise mutual informations:
History
Han (1978) originally defined the dual total correlation as,
However Abdallah and Plumbley (2010) showed its equivalence to the easiertounderstand form of the joint entropy minus the sum of conditional entropies via the following:
See also
This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (June 2011) (Learn how and when to remove this template message)

References
 Han T. S. (1978). Nonnegative entropy measures of multivariate symmetric correlations, Information and Control 36, 133–156.
 Fujishige Satoru (1978). Polymatroidal Dependence Structure of a Set of Random Variables, Information and Control 39, 55–72. doi:10.1016/S00199958(78)91063X.
 Olbrich, E. and Bertschinger, N. and Ay, N. and Jost, J. (2008). How should complexity scale with system size?, The European Physical Journal B  Condensed Matter and Complex Systems. doi:10.1140/epjb/e2008001349.
 Abdallah S. A. and Plumbley, M. D. (2010). A measure of statistical complexity based on predictive information, ArXiv eprints. arXiv:1012.1890v1.
 Nihat Ay, E. Olbrich, N. Bertschinger (2001). A unifying framework for complexity measures of finite systems. European Conference on Complex Systems. pdf.