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Abstract:
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In information theory, the mutual information is defined and fully studied in the past. In this paper, we first introduce the concept of the multivariate information, which extends the concept of mutual information from the case of two (groups of) random variables to the case of multiple (groups of) random variables, and then, K-dependence coefficient is extended to measure the interaction among the random variables using the multivariate information. This paper also shows that a group of random variables can be decomposed into different portions in terms of information. Finally a mathematical expression of a complete decomposition for K-Dependence coefficient is given and proved.
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