Decomposition of the transfer entropy: Partial conditioning and informative clustering

We propose a formal expansion of the transfer entropy to address the problem or partial conditioning evaluating information flow in multivariate datasets. This approach will then be adapted to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by an high value will be associated to informational circuits present in the system, with an informational character (synergetic or redundant) which can be associated to the sign of the contribution. These methods are then applied to the analysis of fMRI data.