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Dual total correlation : ウィキペディア英語版
Dual total correlation

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 non-negative 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 joint-entropy of the ''n'' elements. Although well behaved, dual total correlation has received much less attention than the total correlation. A measure known as "TSE-complexity" defines a continuum between the total correlation and dual total correlation (Ay 2001).
==Definition==

For a set of ''n'' random variables \, the dual total correlation D(X_1,\ldots,X_n) is given by
: D(X_1,\ldots,X_n) = H\left( X_1, \ldots, X_n \right) - \sum_^n H\left( X_i | X_1, \ldots, X_, X_, \ldots, X_n \right) ,
where H(X_,\ldots,X_) is the joint entropy of the variable set \\} and H(X_| ... ) is the conditional entropy of variable X_, given the rest.

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