Given a fixed dependency graph $G$ that describes a Bayesian network of binary variables $X_1,\cdots ,X_n$, our main result is a tight bound on the mutual information $I_c(Y_1,\cdots ,Y_k)={\sum }_{j=1}^{k}H\left(Y_j\right)/c-H(Y_1,\cdots ,Y_k)$ of an observed subset $Y_1,\cdots ,Y_k$ of the variables $X_1,\cdots ,X_n$. Our bound depends on certain quantities that can be computed from the connective structure of the nodes in $G$. Thus it allows to discriminate between different dependency graphs for a probability distribution, as we show from numerical experiments.

Our concern here, is the characterization of dissimilarity indexes defined over finite sets, whose spatial representation is spherical. Consequently, we propose a methodology (Normed MultiDimensional Scaling) to determine the spherical euclidean representation of a set of items best accounting for the initial dissimilarity between items. This methodology has the advantage of being graphically readable on individual qualities of projection like the normed PCA, of which it constitutes a generalization....