Cohesion

The cohesion [RNE+16] is a parameterized multivariate mutual information which spans from the Total Correlation to the Dual Total Correlation:

Note

TODO: confirm whether the canonical reference for cohesion is [RNE+16] (Rosas et al. 2016) or a later Rosas et al. 2019 paper on high-order interdependencies.

\[C_k[X_0 : X_1 : \dotsc : X_n] = \sum_{\substack{A \subset [n]}{|A| = k}} \H{X_A} - \binom{n - 1}{k - 1} \H{X_0, X_1, \dotsc, X_n}\]